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Programming Enigma Puzzles

17 March 2013

Posted by on **From New Scientist #2611, 7th July 2007**

Using a standard set of dominoes, I laid out the chain 0-0 0-1 1-1 1-2 2-2 in one direction so that the total number of “pips” in the chain reached every one of the triangular numbers 1 3 6 10 … in turn up to the greatest possible triangular number.

If there was a choice of routes from one triangular number to the following one (as for example in the next one to that shown, which might be 2-0 0-3 or 2-3), I preferred the route using the smaller or smallest number of dominoes that allowed me to continue. Having reached the highest triangular number that I could in this manner, I found that I had more than five dominoes in my hand left unused.

Which were these dominoes?

[enigma1450]

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This Python program solves the problem recursively. It runs in 36ms.

Solution:The six unused dominoes are 0-2, 0-4, 0-6, 1-4, 1-6 and 2-6.