# Sunday Times Teaser 2932 – Triangulation

*by Andrew Skidmore*

#### Published December 2 2018 (link)

Liam plans to make a set of dominoes. They will be triangular, and one face of each domino will have a number at each corner. The numbers run from 0 up to a maximum digit (9 or less), and the set is to include all possible distinguishable dominoes.

With the maximum digit he has chosen the set would contain a triangular number of dominoes. [A triangular number is one where that number of balls can fit snugly in an equilateral triangle, for example the 15 red balls on a snooker table]

How many dominoes will he need to make?

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Either create the set of distinguishable dominoes and find its length:

or evaluate the formula giving its length: