Listen With Others

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4023: Oyler’s Pentomino Factory (or Painting by Numbers)

Posted by Listen With Others on 20 March 2009

This was the first numerical Listener puzzle the junior coffee break team had attempted. We had heard how dreadfully difficult these numerical puzzles are and were predisposed to settle down with a good book and not even look at No 4023. But we did!

Surprise, surprise! It looked do-able. We heaved a huge sigh of relief – unlike you regulars who felt that this was not a challenge. Thank you, Oyler for sparing a thought for the relative newcomers.

We had to suss out pentominoes first and Googled up the twelve that are different (not counting the rotation and reflection effects that clearly had to be considered). With a little 5 X 12 board, the less mathematical part of the team played with these and soon established that, spatially, fitting them together is no cakewalk. The Internet confirmed that there are 1200 or so possibilities! Meanwhile, Mr Math was working out the factors and sorting out possible positions.

It was obviously clear which nine squares the 0 pentomino had to occupy and which six potential pentominoes could fill that role. The 10 seemed a candidate for the top right hand corner because of all those high numbers in the row and column products and the 11 could be uniquely placed on the other side for the same reason – so now there were five 0 candidates.

The rest took time with the 5 and 3 pentominos required to lurk centrally in the top 2 or 3 rows putting 9 on the lower left, 2 and 7 causing us some concern, and some dithering about the way to fit in the multiples of 2 on the right, but we worked from that side and made it – with astonishment.

Our final challenge was that question of the colouring in. Clearly it makes judging the solutions easier if there are all those pretty colours BUT when we had put in two, could we consider the white spaces to be the third? Is the Listener so tricky? Will the winner have just two colours and white? No – that would be too silly: we decided that ‘colours’ were required and white is not, strictly speaking, a colour or, if it is as Chambers claims ‘the colour of snow’, it counts as a third one. (Incidentally, Mr Chambers hasn’t seen the ‘colour’ of the snow that has been lying in our garden since November!)

Thank you Oyler! After Salamanca’s Mazy, where we got into the maze but never even met the Minotaur and certainly couldn’t put together enough thread to get out, this was very refreshing for the less able gang.

Shirley Curran.

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