Euler problems/41 to 50
(→[http://projecteuler.net/index.php?section=problems&id=46 Problem 46]: solution inspired by SICP exercise 3.70)
Revision as of 05:02, 28 March 2007
What is the largest n-digit pandigital prime that exists?
problem_41 = undefined
How many triangle words can you make using the list of common English words?
problem_42 = undefined
Find the sum of all pandigital numbers with an unusual sub-string divisibility property.
problem_43 = undefined
Find the smallest pair of pentagonal numbers whose sum and difference is pentagonal.
problem_44 = undefined
After 40755, what is the next triangle number that is also pentagonal and hexagonal?
problem_45 = undefined
What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
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
Find the first four consecutive integers to have four distinct primes factors.
problem_47 = undefined
Find the last ten digits of 11 + 22 + ... + 10001000.
problem_48 = undefined
Find arithmetic sequences, made of prime terms, whose four digits are permutations of each other.
problem_49 = undefined
10 Problem 50
Which prime, below one-million, can be written as the sum of the most consecutive primes?
problem_50 = undefined