Difference between revisions of "Euler problems/11 to 20"
(→[http://projecteuler.net/index.php?section=problems&id=16 Problem 16]: fix problem description) |
(→[http://projecteuler.net/index.php?section=problems&id=12 Problem 12]: add a solution) |
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Line 12: | Line 12: | ||
Solution: |
Solution: |
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<haskell> |
<haskell> |
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− | problem_12 = |
+ | problem_12 = head $ filter ((> 500) . nDivisors) triangleNumbers |
+ | where triangleNumbers = scanl1 (+) [1..] |
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+ | nDivisors n = product $ map ((+1) . length) (group (primeFactors n)) |
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+ | primes = 2 : filter ((== 1) . length . primeFactors) [3,5..] |
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+ | primeFactors n = factor n primes |
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+ | where factor n (p:ps) | p*p > n = [n] |
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+ | | n `mod` p == 0 = p : factor (n `div` p) (p:ps) |
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+ | | otherwise = factor n ps |
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</haskell> |
</haskell> |
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Revision as of 01:33, 28 March 2007
Problem 11
What is the greatest product of four numbers on the same straight line in the 20 by 20 grid?
Solution:
problem_11 = undefined
Problem 12
What is the first triangle number to have over five-hundred divisors?
Solution:
problem_12 = head $ filter ((> 500) . nDivisors) triangleNumbers
where triangleNumbers = scanl1 (+) [1..]
nDivisors n = product $ map ((+1) . length) (group (primeFactors n))
primes = 2 : filter ((== 1) . length . primeFactors) [3,5..]
primeFactors n = factor n primes
where factor n (p:ps) | p*p > n = [n]
| n `mod` p == 0 = p : factor (n `div` p) (p:ps)
| otherwise = factor n ps
Problem 13
Find the first ten digits of the sum of one-hundred 50-digit numbers.
Solution:
problem_13 = undefined
Problem 14
Find the longest sequence using a starting number under one million.
Solution:
problem_14 = undefined
Problem 15
Starting in the top left corner in a 20 by 20 grid, how many routes are there to the bottom right corner?
Solution:
problem_15 = undefined
Problem 16
What is the sum of the digits of the number 21000?
Solution:
problem_16 = undefined
Problem 17
How many letters would be needed to write all the numbers in words from 1 to 1000?
Solution:
problem_17 = undefined
Problem 18
Find the maximum sum travelling from the top of the triangle to the base.
Solution:
problem_18 = undefined
Problem 19
How many Sundays fell on the first of the month during the twentieth century?
Solution:
problem_19 = undefined
Problem 20
Find the sum of digits in 100!
Solution:
problem_20 = undefined