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Listener 4699, Pentominoes by Child’s Play

Posted by vaganslistener on 11 Mar 2022

Well, here’s a Numerical Novice’s attempt at PENTOMINOES, which was no Child’s Play for me, though easier to get into than some, and with an element of fun too. I hope the setter will offer us more games soon!

My initial hope was (a) that the tiling would have a unique solution, and (b) that it would be on the web. I did find a neat little wesbite that let me type in the grid complete with holes, but when it reached 100 solutions and still counting I realised that it was a dead end, and got the pencil and rubber out instead.

My way in was through 7a which soon showed that it had a unique solution, locking in two letters, and generating 6561 that I realised – having looked at all those pentominoes flashing before my eyes – had to have its 6’s covered by the U-shape. I then made a table of all the 3-digit products of the relevant primes (thank you Excel) and with the help of that was able to narrow in on 3, 4 and 5d, took a punt that 662 and 668 would be the values for 3 and 4d as they would fit the pentomino pattern. One of the likely primes was 61, and I started to pencil in the U shape of 6s, closely followed by the 1s and 5s and so on.

I did grind away at the spreadsheet to pick out some other clue answers, but frankly my skill-set made it much easier to deduce the pentomino pattern and reverse engineer the calculations. As some of them could apply to more than one answer – and as there was no way I was going to work out a Single Logical Path – there was en element of guesswork and special pleading here, and at the end I was still left with one that I couldn’t explain even though I was sure the solution was right.

These are never going to be my cup of tea – there is usually too much detailed calculation and recording and not enough intuition involved for me – but the bricks won the day, and many thanks to Child’s Play for getting them out of the box.


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