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Good Try

One thought, with Russell Dear [Neurobics, August 1993], can Tom Duerden's product square puzzle be solved in smaller integers?

My square uses smaller distinct integers than Mr Duerden's list, only replacing his multiples 7, 14, 21, 28 by powers 8, 9, 16, 27. So I changed 28 in their diagram to 12 in mine.

Product square:

10 3 6 24
16 9 15 2
27 8 4 5
1 20 12 18

Rows and columns now all multiply to 4320 instead of 5040. It appeared that Mr Dear had suspected wrongly that his square had the least product for a four-by-four product square!

But however I permuted the rows and columns of my solution (24 ways), the diagonals could not be made to equal 4320 as well. I suspect Russell Dear knew all along!

Donald S. McDonald, Wellington