Difference between revisions of "Euler problems"
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| − | It is recommended you try them yourself before looking at the solutions as these form good exercises for improving your Haskell- |
+ | It is recommended you try them yourself before looking at the solutions as these form good exercises for improving your Haskell-fu. |
| + | * [[EulerProblems/1_to_10|Questions 1 to 10]] |
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| − | |||
| + | * [[EulerProblems/11_to_20|Questions 11 to 20]] |
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| − | == [http://projecteuler.net/index.php?section=problems&id=1 Problem 1] == |
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| + | * [[EulerProblems/21_to_30|Questions 21 to 30]] |
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| − | Add all the natural numbers below 1000 that are multiples of 3 or 5. |
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| + | * [[EulerProblems/31_to_40|Questions 31 to 40]] |
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| − | |||
| + | * [[EulerProblems/41_to_50|Questions 41 to 50]] |
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| − | Solution: |
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| + | * [[EulerProblems/51_to_60|Questions 51 to 60]] |
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| − | <haskell> |
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| + | * [[EulerProblems/61_to_70|Questions 61 to 70]] |
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| − | problem_1 = sum [ x | x <- [1..1000], x `mod` 3 == 0, x `mod` 5 == 0] |
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| + | * [[EulerProblems/71_to_80|Questions 71 to 80]] |
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| − | </haskell> |
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| + | * [[EulerProblems/81_to_90|Questions 81 to 90]] |
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| − | |||
| + | * [[EulerProblems/91_to_100|Questions 91 to 100]] |
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| − | == [http://projecteuler.net/index.php?section=problems&id=2 Problem 2] == |
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| + | * [[EulerProblems/101_to_110|Questions 101 to 110]] |
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| − | Find the sum of all the even-valued terms in the Fibonacci sequence which do not exceed one million. |
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| + | * [[EulerProblems/111_to_120|Questions 111 to 120]] |
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| − | |||
| + | * [[EulerProblems/121_to_130|Questions 121 to 130]] |
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| − | Solution: |
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| + | * [[EulerProblems/131_to_140|Questions 131 to 140]] |
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| − | <haskell> |
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| + | * [[EulerProblems/141_to_146|Questions 141 to 146]] |
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| − | problem_2 = sum [ x | x <- fibs, x `mod` 2 == 0] |
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| − | where fibs = 1 : 1 : zipWith (+) fibs (tail fibs) |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=3 Problem 3] == |
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| − | Find the largest prime factor of 317584931803. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_3 = foldr max 0 [ x | x <- [1..(round $ sqrt c)], c `mod` x == 0] |
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| − | where c = 317584931803 |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=4 Problem 4] == |
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| − | Find the largest palindrome made from the product of two 3-digit numbers. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_4 = foldr max 0 [ x | y <- [100..999], z <- [100..999], let x = y * z, let s = show x, s == reverse s] |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=5 Problem 5] == |
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| − | What is the smallest number divisible by each of the numbers 1 to 20? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_5 = head [ x | x <- [2520,5040..], all (\y -> x `mod` y == 0) [1..20]] |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=6 Problem 6] == |
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| − | What is the difference between the sum of the squares and the square of the sums? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_6 = sum [ x^2 | x <- [1..100]] - (sum [1..100])^2 |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=7 Problem 7] == |
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| − | Find the 10001st prime. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_7 = head $ drop 10000 primes |
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| − | where primes = 2:3:.. |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=8 Problem 8] == |
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| − | Discover the largest product of five consecutive digits in the 1000-digit number. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_8 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=9 Problem 9] == |
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| − | Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_9 = head [a*b*c | a <- [1..500], b <- [a..500], c <- [1..(1000-a-b)], a + b + c == 1000, a^2 + b^2 == c^2] |
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| − | </haskell> |
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| − | |||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=10 Problem 10] == |
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| − | Calculate the sum of all the primes below one million. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_10 = sum [ p | p <- primes, p < 1000000 ] |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=11 Problem 11] == |
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| − | What is the greatest product of four numbers on the same straight line in the 20 by 20 grid? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_11 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=12 Problem 12] == |
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| − | What is the first triangle number to have over five-hundred divisors? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_12 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=13 Problem 13] == |
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| − | Find the first ten digits of the sum of one-hundred 50-digit numbers. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_13 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=14 Problem 14] == |
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| − | Find the longest sequence using a starting number under one million. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_14 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=15 Problem 15] == |
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| − | Starting in the top left corner in a 20 by 20 grid, how many routes are there to the bottom right corner? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_15 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=16 Problem 16] == |
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| − | What is the sum of the digits of the number 21000? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_16 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=17 Problem 17] == |
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| − | How many letters would be needed to write all the numbers in words from 1 to 1000? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_17 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=18 Problem 18] == |
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| − | Find the maximum sum travelling from the top of the triangle to the base. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_18 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=19 Problem 19] == |
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| − | How many Sundays fell on the first of the month during the twentieth century? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_19 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=20 Problem 20] == |
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| − | Find the sum of digits in 100! |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_20 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=21 Problem 21] == |
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| − | Evaluate the sum of all amicable pairs under 10000. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_21 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=22 Problem 22] == |
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| − | What is the total of all the name scores in the file of first names? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_22 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=23 Problem 23] == |
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| − | Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_23 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=24 Problem 24] == |
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| − | What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_24 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=25 Problem 25] == |
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| − | What is the first term in the Fibonacci sequence to contain 1000 digits? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_25 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=26 Problem 26] == |
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| − | Find the value of d < 1000 for which 1/d contains the longest recurring cycle. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_26 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=27 Problem 27] == |
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| − | Find a quadratic formula that produces the maximum number of primes for consecutive values of n. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_27 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=28 Problem 28] == |
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| − | What is the sum of both diagonals in a 1001 by 1001 spiral? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_28 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=29 Problem 29] == |
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| − | How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_29 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=30 Problem 30] == |
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| − | Find the sum of all the numbers that can be written as the sum of fifth powers of their digits. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_30 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=31 Problem 31] == |
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| − | Investigating combinations of English currency denominations. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_31 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=32 Problem 32] == |
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| − | Find the sum of all numbers that can be written as pandigital products. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_32 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=33 Problem 33] == |
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| − | Discover all the fractions with an unorthodox cancelling method. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_33 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=34 Problem 34] == |
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| − | Find the sum of all numbers which are equal to the sum of the factorial of their digits. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_34 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=35 Problem 35] == |
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| − | How many circular primes are there below one million? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_35 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=36 Problem 36] == |
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| − | Find the sum of all numbers less than one million, which are palindromic in base 10 and base 2. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_36 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=37 Problem 37] == |
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| − | Find the sum of all eleven primes that are both truncatable from left to right and right to left. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_37 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=38 Problem 38] == |
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| − | What is the largest 1 to 9 pandigital that can be formed by multiplying a fixed number by 1, 2, 3, ... ? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_38 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=39 Problem 39] == |
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| − | If p is the perimeter of a right angle triangle, {a, b, c}, which value, for p ≤ 1000, has the most solutions? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_39 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=40 Problem 40] == |
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| − | Finding the nth digit of the fractional part of the irrational number. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_40 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=41 Problem 41] == |
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| − | What is the largest n-digit pandigital prime that exists? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_41 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=42 Problem 42] == |
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| − | How many triangle words can you make using the list of common English words? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_42 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=43 Problem 43] == |
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| − | Find the sum of all pandigital numbers with an unusual sub-string divisibility property. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_43 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=44 Problem 44] == |
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| − | Find the smallest pair of pentagonal numbers whose sum and difference is pentagonal. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_44 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=45 Problem 45] == |
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| − | After 40755, what is the next triangle number that is also pentagonal and hexagonal? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_45 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=46 Problem 46] == |
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| − | What is the smallest odd composite that cannot be written as the sum of a prime and twice a square? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_46 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=47 Problem 47] == |
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| − | Find the first four consecutive integers to have four distinct primes factors. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_47 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=48 Problem 48] == |
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| − | Find the last ten digits of 11 + 22 + ... + 10001000. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_48 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=49 Problem 49] == |
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| − | Find arithmetic sequences, made of prime terms, whose four digits are permutations of each other. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_49 = undefined |
||
| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=50 Problem 50] == |
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| − | Which prime, below one-million, can be written as the sum of the most consecutive primes? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_50 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=51 Problem 51] == |
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| − | Find the smallest prime which, by changing the same part of the number, can form eight different primes. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
||
| − | problem_51 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=52 Problem 52] == |
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| − | Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits in some order. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_52 = undefined |
||
| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=53 Problem 53] == |
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| − | How many values of C(n,r), for 1 ≤ n ≤ 100, exceed one-million? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_53 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=54 Problem 54] == |
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| − | How many hands did player one win in the game of poker? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
||
| − | problem_54 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=55 Problem 55] == |
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| − | How many Lychrel numbers are there below ten-thousand? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_55 = undefined |
||
| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=56 Problem 56] == |
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| − | Considering natural numbers of the form, ab, finding the maximum digital sum. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_56 = undefined |
||
| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=57 Problem 57] == |
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| − | Investigate the expansion of the continued fraction for the square root of two. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
||
| − | problem_57 = undefined |
||
| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=58 Problem 58] == |
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| − | Investigate the number of primes that lie on the diagonals of the spiral grid. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
||
| − | problem_58 = undefined |
||
| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=59 Problem 59] == |
||
| − | Using a brute force attack, can you decrypt the cipher using XOR encryption? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_59 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=60 Problem 60] == |
||
| − | Find a set of five primes for which any two primes concatenate to produce another prime. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_60 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=61 Problem 61] == |
||
| − | Find the sum of the only set of six 4-digit figurate numbers with a cyclic property. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_61 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=62 Problem 62] == |
||
| − | Find the smallest cube for which exactly five permutations of its digits are cube. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_62 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=63 Problem 63] == |
||
| − | How many n-digit positive integers exist which are also an nth power? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_63 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=64 Problem 64] == |
||
| − | How many continued fractions for N ≤ 10000 have an odd period? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_64 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=65 Problem 65] == |
||
| − | Find the sum of digits in the numerator of the 100th convergent of the continued fraction for e. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_65 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=66 Problem 66] == |
||
| − | Investigate the Diophantine equation x2 − Dy2 = 1. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_66 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=67 Problem 67] == |
||
| − | Using an efficient algorithm find the maximal sum in the triangle? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_67 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=68 Problem 68] == |
||
| − | What is the maximum 16-digit string for a "magic" 5-gon ring? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_68 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=69 Problem 69] == |
||
| − | Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_69 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=70 Problem 70] == |
||
| − | Investigate values of n for which φ(n) is a permutation of n. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_70 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=71 Problem 71] == |
||
| − | Listing reduced proper fractions in ascending order of size. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_71 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=72 Problem 72] == |
||
| − | How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_72 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=73 Problem 73] == |
||
| − | How many fractions lie between 1/3 and 1/2 in a sorted set of reduced proper fractions? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_73 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=74 Problem 74] == |
||
| − | Determine the number of factorial chains that contain exactly sixty non-repeating terms. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_74 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=75 Problem 75] == |
||
| − | Find the number of different lengths of wire can that can form a right angle triangle in only one way. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_75 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=76 Problem 76] == |
||
| − | How many different ways can one hundred be written as a sum of at least two positive integers? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_76 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=77 Problem 77] == |
||
| − | What is the first value which can be written as the sum of primes in over five thousand different ways? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_77 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=78 Problem 78] == |
||
| − | Investigating the number of ways in which coins can be separated into piles. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_78 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=79 Problem 79] == |
||
| − | By analysing a user's login attempts, can you determine the secret numeric passcode? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_79 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=80 Problem 80] == |
||
| − | Calculating the digital sum of the decimal digits of irrational square roots. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_80 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=81 Problem 81] == |
||
| − | Find the minimal path sum from the top left to the bottom right by moving right and down. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_81 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=82 Problem 82] == |
||
| − | Find the minimal path sum from the left column to the right column. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_82 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=83 Problem 83] == |
||
| − | Find the minimal path sum from the top left to the bottom right by moving left, right, up, and down. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_83 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=84 Problem 84] == |
||
| − | In the game, Monopoly, find the three most popular squares when using two 4-sided dice. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_84 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=85 Problem 85] == |
||
| − | Investigating the number of rectangles in a rectangular grid. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_85 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=86 Problem 86] == |
||
| − | Exploring the shortest path from one corner of a cuboid to another. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_86 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=87 Problem 87] == |
||
| − | Investigating numbers that can be expressed as the sum of a prime square, cube, and fourth power? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_87 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=88 Problem 88] == |
||
| − | Exploring minimal product-sum numbers for sets of different sizes. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_88 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=89 Problem 89] == |
||
| − | Develop a method to express Roman numerals in minimal form. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_89 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=90 Problem 90] == |
||
| − | An unexpected way of using two cubes to make a square. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_90 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=91 Problem 91] == |
||
| − | Find the number of right angle triangles in the quadrant. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_91 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=92 Problem 92] == |
||
| − | Investigating a square digits number chain with a surprising property. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_92 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=93 Problem 93] == |
||
| − | Using four distinct digits and the rules of arithmetic, find the longest sequence of target numbers. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_93 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=94 Problem 94] == |
||
| − | Investigating almost equilateral triangles with integral sides and area. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_94 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=95 Problem 95] == |
||
| − | Find the smallest member of the longest amicable chain with no element exceeding one million. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_95 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=96 Problem 96] == |
||
| − | Devise an algorithm for solving Su Doku puzzles. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_96 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=97 Problem 97] == |
||
| − | Find the last ten digits of the non-Mersenne prime: 28433 × 27830457 + 1. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_97 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=98 Problem 98] == |
||
| − | Investigating words, and their anagrams, which can represent square numbers. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_98 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=99 Problem 99] == |
||
| − | Which base/exponent pair in the file has the greatest numerical value? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_99 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=100 Problem 100] == |
||
| − | Finding the number of blue discs for which there is 50% chance of taking two blue. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_100 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=101 Problem 101] == |
||
| − | Investigate the optimum polynomial function to model the first k terms of a given sequence. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_101 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=102 Problem 102] == |
||
| − | For how many triangles in the text file does the interior contain the origin? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_102 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=103 Problem 103] == |
||
| − | Investigating sets with a special subset sum property. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_103 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=104 Problem 104] == |
||
| − | Finding Fibonacci numbers for which the first and last nine digits are pandigital. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_104 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=105 Problem 105] == |
||
| − | Find the sum of the special sum sets in the file. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_105 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=106 Problem 106] == |
||
| − | Find the minimum number of comparisons needed to identify special sum sets. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_106 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=107 Problem 107] == |
||
| − | Determining the most efficient way to connect the network. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_107 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=108 Problem 108] == |
||
| − | Solving the Diophantine equation 1/x + 1/y = 1/n. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_108 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=109 Problem 109] == |
||
| − | How many distinct ways can a player checkout in the game of darts with a score of less than 100? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_109 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=110 Problem 110] == |
||
| − | Find an efficient algorithm to analyse the number of solutions of the equation 1/x + 1/y = 1/n. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_110 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=111 Problem 111] == |
||
| − | Search for 10-digit primes containing the maximum number of repeated digits. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_111 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=112 Problem 112] == |
||
| − | Investigating the density of "bouncy" numbers. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_112 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=113 Problem 113] == |
||
| − | How many numbers below a googol (10100) are not "bouncy"? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_113 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=114 Problem 114] == |
||
| − | Investigating the number of ways to fill a row with separated blocks that are at least three units long. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_114 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=115 Problem 115] == |
||
| − | Finding a generalisation for the number of ways to fill a row with separated blocks. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_115 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=116 Problem 116] == |
||
| − | Investigating the number of ways of replacing square tiles with one of three coloured tiles. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_116 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=117 Problem 117] == |
||
| − | Investigating the number of ways of tiling a row using different-sized tiles. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_117 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=118 Problem 118] == |
||
| − | Exploring the number of ways in which sets containing prime elements can be made. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_118 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=119 Problem 119] == |
||
| − | Investigating the numbers which are equal to sum of their digits raised to some power. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_119 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=120 Problem 120] == |
||
| − | Finding the maximum remainder when (a − 1)n + (a + 1)n is divided by a2. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_120 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=121 Problem 121] == |
||
| − | Investigate the game of chance involving coloured discs. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_121 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=122 Problem 122] == |
||
| − | Finding the most efficient exponentiation method. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_122 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=123 Problem 123] == |
||
| − | Determining the remainder when (pn − 1)n + (pn + 1)n is divided by pn2. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_123 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=124 Problem 124] == |
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| − | Determining the kth element of the sorted radical function. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
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| − | problem_124 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=125 Problem 125] == |
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| − | Finding square sums that are palindromic. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
||
| − | problem_125 = undefined |
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| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=126 Problem 126] == |
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| − | Exploring the number of cubes required to cover every visible face on a cuboid. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
||
| − | problem_126 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=127 Problem 127] == |
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| − | Investigating the number of abc-hits below a given limit. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
||
| − | problem_127 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=128 Problem 128] == |
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| − | Which tiles in the hexagonal arrangement have prime differences with neighbours? |
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| − | |||
| − | Solution: |
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| − | <haskell> |
||
| − | problem_128 = undefined |
||
| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=129 Problem 129] == |
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| − | Investigating minimal repunits that divide by n. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
||
| − | problem_129 = undefined |
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| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=130 Problem 130] == |
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| − | Finding composite values, n, for which n−1 is divisible by the length of the smallest repunits that divide it. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
||
| − | problem_130 = undefined |
||
| − | </haskell> |
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| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=131 Problem 131] == |
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| − | Determining primes, p, for which n3 + n2p is a perfect cube. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
||
| − | problem_131 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=132 Problem 132] == |
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| − | Determining the first forty prime factors of a very large repunit. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
||
| − | problem_132 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=133 Problem 133] == |
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| − | Investigating which primes will never divide a repunit containing 10n digits. |
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| − | |||
| − | Solution: |
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| − | <haskell> |
||
| − | problem_133 = undefined |
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| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=134 Problem 134] == |
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| − | Finding the smallest positive integer related to any pair of consecutive primes. |
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| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_134 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=135 Problem 135] == |
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| − | Determining the number of solutions of the equation x2 − y2 − z2 = n. |
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| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_135 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=136 Problem 136] == |
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| − | Discover when the equation x2 − y2 − z2 = n has a unique solution. |
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| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_136 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=137 Problem 137] == |
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| − | Determining the value of infinite polynomial series for which the coefficients are Fibonacci numbers. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_137 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=138 Problem 138] == |
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| − | Investigating isosceles triangle for which the height and base length differ by one. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_138 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=139 Problem 139] == |
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| − | Finding Pythagorean triangles which allow the square on the hypotenuse square to be tiled. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_139 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=140 Problem 140] == |
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| − | Investigating the value of infinite polynomial series for which the coefficients are a linear second order recurrence relation. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_140 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=141 Problem 141] == |
||
| − | Investigating progressive numbers, n, which are also square. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_141 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=142 Problem 142] == |
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| − | Perfect Square Collection |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_142 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=143 Problem 143] == |
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| − | Investigating the Torricelli point of a triangle |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_143 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=144 Problem 144] == |
||
| − | Investigating multiple reflections of a laser beam. |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_144 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=145 Problem 145] == |
||
| − | How many reversible numbers are there below one-billion? |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_145 = undefined |
||
| − | </haskell> |
||
| − | |||
| − | == [http://projecteuler.net/index.php?section=problems&id=146 Problem 146] == |
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| − | Investigating a Prime Pattern |
||
| − | |||
| − | Solution: |
||
| − | <haskell> |
||
| − | problem_146 = undefined |
||
| − | </haskell> |
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| − | |||
| − | |||
| − | |||
| − | |||
| − | [[Category:Tutorials]] |
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| − | [[Category:Code]] |
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Revision as of 08:18, 27 March 2007
These are the solutions to the problems listed on Project Euler
It is recommended you try them yourself before looking at the solutions as these form good exercises for improving your Haskell-fu.