Enigma 1374: Dominoes to the power of two
10 November 2013
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From New Scientist #2534, 14th January 2006
Using a standard set of dominoes, I laid out a row end-to-end such that (in typical domino style) touching ends were the same (e.g. 6-3, 3-5, 5-5, 5-1 etc). I started with 0-0 and then added dominoes so that the total number of pips in the row equalled 1, then 4, then 9, working my way though each perfect square and continuing as far as possible. My row could not have been shorter at any stage.
Having reached the highest square possible I was left with five dominoes, four of which were doubles.
What were those five dominoes?