# 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?

[enigma1563]

### 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)))
break
```

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

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