Enigmatic Code

Programming Enigma Puzzles

Enigma 1563: Drawing a line

From New Scientist #2726, 19th September 2009 [link]

Enigma is a piece of contemporary art. It consists of a solid white cuboid of sides 18 centimetres, 24 centimetres and some other length (which is not a whole number of centimetres).

On each face of the cuboid there is a straight red line a whole number of centimetres long going from the mid-point of one edge to the mid-point of another. The six lines together form a continuous route over the surface of the cuboid. The shortest two of the lines are of different lengths.

What are the lengths of the six lines?


One response to “Enigma 1563: Drawing a line

  1. jimrandell 22 February 2012 at 11:43 am

    The following Python program runs in 36ms.

    from itertools import count
    from enigma import sqrt, is_square
    # side semi-length c is not a whole number, so we need to
    # find hypotenuses with both the other sides that are
    # if the two shortest lines are different lengths they are
    # across the 18 and 24 cm faces, so we can start looking
    # for hypotenuses 25cm or longer.
    (a, b) = (9, 12)
    for hac in count(25):
      hbc = is_square(b * b + hac * hac - a * a)
      if not hbc: continue
      # what is the third dimension?
      print("2c", "=", 2 * sqrt(hac * hac - a * a))
      # print the length of the lines
      print("lines:", sorted((2 * a, hbc, hac, 2 * b, hac, hbc)))

    Solution: The lengths of the lines are 18cm, 24cm, 31cm, 31cm, 32cm and 32cm.

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