Enigma 1592: Seeing spots
22 January 2012
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From New Scientist #2757, 24th April 2010 [link]
If you take a domino set and discard all those dominoes which involve a 5 or a 6, leaving 15 dominoes with a 0, 1, 2, 3 or 4 at each end, then the rest can be laid out, spotty sides up, to form a 5-by-6 rectangle. Then, taking the number of spots in each square as that square’s value, the product of each row can be calculated by multiplying together the values of the six squares in that row.
Your task is to lay out the dominoes so that the five products are all different, less than 1000, and in increasing order as you come down the rectangle. Just one row must have a product which is odd, just one must have a product which is a power of 2, and just one other must have a product which is a non-zero perfect square.
List the products of the five rows.