Enigmatic Code

Programming Enigma Puzzles

Enigma 1459: Twelve elevenths

From New Scientist #2620, 8th September 2007

If we assume that 11 metres = 12 yards, what is the smallest integral number of metres that can be converted to its equivalent integral number of yards simply by rearranging the order of the digits of the number?

[enigma1459]

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3 responses to “Enigma 1459: Twelve elevenths

  1. Jim Randell 24 February 2013 at 10:24 am

    This is a simple puzzle to solve programatically. The following Python code runs in 36ms. It assumes that the number of metres is a positive integer.

    from itertools import count
    from enigma import printf
    
    for n in count(1):
      (m, y) = (11 * n, 12 * n)
      if sorted(str(m)) == sorted(str(y)):
        printf("{m} metres = {y} yards")
        break
    

    Solution: 1683 metres = 1836 yards.

  2. Naim Uygun 24 February 2013 at 11:13 am
    for meters in range(11,2000,11):
        yards=12*(meters//11)
        sm=sorted(list(str(meters)))
        sy=sorted(list(str(yards)))
        if sm==sy:
           print(meters,yards)
           break
    
  3. Hugh Casement 6 December 2014 at 4:02 pm

    A further solution would be 5724 yards = 5247 m. There are many more if we go to larger numbers.

    But I have to say it’s a lousy conversion factor. 35 yards = 32 m would be a much closer rule-of-thumb approximation. I haven’t found any “anagram” conversions using four digits or fewer.

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