Sunday Times Teaser 2703 – Bastille Day

1. 
   brian gladman permalink

   Python

   from itertools import permutations from fractions import gcd # calculate the proportion for town 'nbr' (1, 2 or 3) def fr(nbr): # counts for all numbers and those divisible by 5 count_all = count_five = 0 # look at all permutations of digits for this town for p in permutations('1234567890'[:-nbr]): n = int(''.join(p)) # consider only those divisible by 11 if n % 11 == 0: count_all += 1 # and count which of these is also divisible by 5 if n % 5 == 0: count_five += 1 # remove any common factor of the counts g = gcd(count_five, count_all) return '{} in {}'.format(count_five // g, count_all // g) print('(A) {}, (B) {}, (C) {}.'.format(fr(1), fr(2), fr(3)))

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   from itertools import permutations from fractions import gcd   # calculate the proportion for town 'nbr' (1, 2 or 3) def fr(nbr):   # counts for all numbers and those divisible by 5   count_all = count_five = 0   # look at all permutations of digits for this town   for p in permutations('1234567890'[:-nbr]):     n = int(''.join(p))     # consider only those divisible by 11     if n % 11 == 0:       count_all += 1       # and count which of these is also divisible by 5       if n % 5 == 0:         count_five += 1   # remove any common factor of the counts   g = gcd(count_five, count_all)   return '{} in {}'.format(count_five // g, count_all // g)   print('(A) {}, (B) {}, (C) {}.'.format(fr(1), fr(2), fr(3)))

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