76629 sbp #!/usr/bin/env python def sums(a, b, c, d): if (a + b + c) == d: return True return False sums_true = set() def descending(a, b, c, d): if (a > b) and (b > c): return True return False descending_true = set() def even(a, b, c, d): e = list(sorted([a % 2, b % 2, c % 2, d % 2])) if e == [0, 0, 1, 1]: return True return False even_true = set() def primes(a, b, c, d): n = 0 p = set([2, 3, 5, 7]) for num in (a, b, c, d): if num in p: n += 1 return n == 2 primes_true = set() def squares(a, b, c, d): n = 0 s = set([1, 4, 9]) for num in (a, b, c, d): if num in s: n += 1 return n == 2 squares_true = set() for i in xrange(1000, 10000): nums = str(i) a, b, c, d = map(int, nums) if sums(a, b, c, d): sums_true.add(i) if descending(a, b, c, d): descending_true.add(i) if even(a, b, c, d): even_true.add(i) if primes(a, b, c, d): primes_true.add(i) if squares(a, b, c, d): squares_true.add(i) print 'Sums:', len(sums_true) print 'Descending:', len(descending_true) print 'Even:', len(even_true) print 'Primes:', len(primes_true) print 'Squares:', len(squares_true) print print 'Sums & Descending:', len(sums_true & descending_true) print 'Sums & Even:', len(sums_true & even_true) print 'Sums & Primes:', len(sums_true & primes_true) print 'Sums & Squares:', len(sums_true & squares_true) print 'Descending & Even:', len(descending_true & even_true) print 'Descending & Primes:', len(descending_true & primes_true) print 'Descending & Squares:', len(descending_true & squares_true) print 'Even & Primes:', len(even_true & primes_true) print 'Even & Squares:', len(even_true & squares_true) print 'Primes & Squares:', len(primes_true & squares_true) print all = len(sums_true & descending_true & even_true & primes_true & squares_true) print 'All:', all 3445442182 #swhack None TRUE 1 sbp Sums: 165 Descending: 1200 Even: 3375 Primes: 3168 Squares: 2457 Sums & Descending: 23 Sums & Even: 125 Sums & Primes: 63 Sums & Squares: 62 Descending & Even: 500 Descending & Primes: 456 Descending & Squares: 336 Even & Primes: 1320 Even & Squares: 930 Primes & Squares: 864 All: 2 3445442222 #swhack TRUE