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Programming Enigma Puzzles

19 September 2014

Posted by on **From New Scientist #2450, 5th June 2004** [link]

Susan Denham‘s recent Enigma “Natural Numbers” prompted me to look for a French version. Once again I have assigned a number to each letter of the alphabet and the numbers, which are not all different, include negative numbers, zero, positive numbers and fractions.

I can tell you that:

U + N = 1

D + E + U + X = 2

T + R + O + I + S = 3

Q + U + A + T + R + E = 4

C + I + N + Q = 5

S + I + X = 6

S + E + P + T = 7

H + U + I + T = 8

N + E + U + F = 9

D + I + X = 10

O + N + Z + E = 11

D + O + U + Z + E = 12

T + R + E + I + Z + E = 13

Q + U + A + T + O + R + Z + E = 14

Q + U + I + N + Z + E = 15Please send in S + A + I + N + T + T + R + O + P + E + Z.

**Note:** I am waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment. The current estimate is that the line will be connected at the end of September 2014.

[enigma1292]

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I used the SymPy symbolic maths library to solve the simultaneous equations for me.

This Python program runs in 487ms.

Solution:S + A + I + N + T + T + R + O + P + E + Z = 33.We can’t work out the actual values of all the letters, but we can determine their values in terms of T and Z.

In the required sum the coefficients of T and Z turn out to be zero, so the numerical value of the sum can be calculated.

Here’s an LP solution using the same

PyMathProgcode I used forEnigma 1278. It runs in 52ms.The multipliers it finds are:

(3/2)×[1] – 2×[2] – (1/2)×[3] + (1/2)×[4] + (1/2)×[6] + [7] + (3/2)×[10] + (1/2)×[11] + (1/2)×[12] + (1/2)×[13] + (1/2)×[14] – [15] = 33.

The French for 13 is treize. I know it makes no difference to the letters count, but I still think words should be correctly spelled.

Oops! There is a mistake in the transcription. It was published correctly in the magazine. I’ve now corrected it.

Thanks for pointing out the mistake.