Difference between revisions of "Euler problems/41 to 50"
(→[http://projecteuler.net/index.php?section=problems&id=46 Problem 46]: solution inspired by SICP exercise 3.70) 
BrettGiles (talk  contribs) m (EulerProblems/41 to 50 moved to Euler problems/41 to 50) 
(No difference)

Revision as of 00:23, 29 March 2007
Contents
Problem 41
What is the largest ndigit pandigital prime that exists?
Solution:
problem_41 = undefined
Problem 42
How many triangle words can you make using the list of common English words?
Solution:
problem_42 = undefined
Problem 43
Find the sum of all pandigital numbers with an unusual substring divisibility property.
Solution:
problem_43 = undefined
Problem 44
Find the smallest pair of pentagonal numbers whose sum and difference is pentagonal.
Solution:
problem_44 = undefined
Problem 45
After 40755, what is the next triangle number that is also pentagonal and hexagonal?
Solution:
problem_45 = undefined
Problem 46
What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
Solution:
This solution is inspired by exercise 3.70 in Structure and Interpretation of Computer Programs, (2nd ed.).
problem_46 = head $ oddComposites `orderedDiff` gbSums
oddComposites = filter ((>1) . length . primeFactors) [3,5..]
gbSums = map gbWeight $ weightedPairs gbWeight primes [2*n*n  n < [1..]]
gbWeight (a,b) = a + b
weightedPairs w (x:xs) (y:ys) =
(x,y) : mergeWeighted w (map ((,)x) ys) (weightedPairs w xs (y:ys))
mergeWeighted w (x:xs) (y:ys)
 w x <= w y = x : mergeWeighted w xs (y:ys)
 otherwise = y : mergeWeighted w (x:xs) ys
x `orderedDiff` [] = x
[] `orderedDiff` y = []
(x:xs) `orderedDiff` (y:ys)
 x < y = x : xs `orderedDiff` (y:ys)
 x > y = (x:xs) `orderedDiff` ys
 otherwise = xs `orderedDiff` ys
Problem 47
Find the first four consecutive integers to have four distinct primes factors.
Solution:
problem_47 = undefined
Problem 48
Find the last ten digits of 11 + 22 + ... + 10001000.
Solution:
problem_48 = undefined
Problem 49
Find arithmetic sequences, made of prime terms, whose four digits are permutations of each other.
Solution:
problem_49 = undefined
Problem 50
Which prime, below onemillion, can be written as the sum of the most consecutive primes?
Solution:
problem_50 = undefined