**From New Scientist #2458, 31st July 2004**

This puzzle has appeared as an Enigma puzzle in both English and French versions, but incredibly it also works in Portuguese.

Triangular numbers are those that fit the formula n×(n+1)/2, like 1, 3, 6 and 10. In the following statement digits have been consistently replaced by capital letters, different letters being used for different digits: UM, TRES, SEIS, DEZ are all triangular numbers, none of which starts with a zero.

Which numbers are represented (in this order) by UM, TRES, SEIS, and DEZ?

**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.

[enigma1300]

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This Python program runs in 34ms.

Solution:UM=45, TRES=2701, SEIS=1081, DEZ=903.Or using the [[

`SubstitutedExpression()`

]] solver from theenigma.pylibrary.This run file executes in 123ms.

A permutation solution gives the same answer: