## Zag Numerical Playfair

Posted by shirleycurran on 9 Jun 2017

What a neat little numerical grid! That was my first reaction on downloading Zag’s crossword but then, with horror, I saw that little Playfair code-square alongside it and read the title. Surely this must be a nightmare! There’s a current Zag numerical puzzle in the Magpie where answers have to be squared and jumbled. I didn’t think things could get much worse than that … but a Playfair numerical. What is the Listener coming to! I couldn’t even read through the clues to check Zag’s membership of the Listener drinkie club (though his final grid did have a 69 in it on the bottom row and I suppose, at a stretch, he could be downing Vat 69 – Cheers, anyway, Zag!

We muttered and squabbled and moaned and shouted for ages as we simply couldn’t see the way in and I showed my habitual incomprehension of Playfair code-squares. The other Numpty patiently explained several times, then realized that whatever the code number (which we were told was two digits that had to be entered encoded at 9ac) it had to encode to X1 X2 or X3, and, since 6d was a 3-digit square, neither 3 nor 2 could be its third digit. We had potential 121, 361, 441, 841 and 961.

One digit was established. Now what? 3d was the reverse of 2ac and while I tried to get my calculator to give me numbers that would fulfil that and produce a divisor of 3d at 7ac that would give a corresponding second digit, the other Numpty wrote a mini programme that produced the same two numbers that I came up with; 966, which gave a divisor of 166, and 855 which gave 186. Those were the only two that would give a possible answer for 2dn where we had to add the digits of 7ac and get a double figure.

By sheer luck, I opted for the 855 route that led me to 186, adding to 15. The 1 encoding to 8 was already established and I now drew up two putative Playfair code-squares. Since we knew that 8 was the first digit of 2d, there was a fair chance that 9 would be the second which would give 234 and 567 as two rows of one putative Playfair code-square. I shouted with delight when a 567 row and a 936 column appeared in one of my two. (Obviously we knew that 5d had to have 1,3,6, or 9 as its centre digit which confirmed that this was the code-square to use.) So 89 was our code-number, encoding to 91 at 9ac. and 361 (19 squared) was the choice at 6d. 7d had appeared and our Playfair square told us that 16 was 97, encripted – the required prime of the clue. We had three empty cells and 1d and 1ac to complete. One of them had to be a divisor of 855 since nothing else in the grid was, which gave us 150 for 1d and 19 for 1ac. A final check told us that our digits added to 98, which, of course, encoded to 19. Dare I admit that I actually enjoyed this numerical? (Good grief, Zag will probably be encouraged to put all of his next one into Playfair and jumble the clues too!) All the same, thank you, Zag.

How could a hare have crept into that grid?

Any wise hare would be hiding well behind the grid; but there he was, alphanumerically converted (8 1 18 5) and rather jumbled but maintaining the Listener golden hare tradition.

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