# Listen With Others

## Pairs by Elap

Posted by shirleycurran on 12 June 2015

The penultimate week of February, May, August and November – the dreaded numericals. I download it and dash away, handing over to the other Numpty. Not much chance of even checking for Elap’s membership of the Listener Setter’s toper’s crowd. The clues read ‘FLY!’ (which I do) and Grr! which, I admit, is my usual reaction to the hated things – though, of course ‘bottoms up, Elap!’ and you get PALE, or, with the top removed, just ALE, so I suppose he has automatic membership.

Numpty No 1 applies his usual logic and Zipf’s law of frequencies which suggests that the likely ranking is going to be I, Y, E, X, L, G, S, F, T. Very soon there is a restriction on I and Y. Y can’t be greater than 9 (19ac) and I has to be less than 10 (13dn) so I and Y are 1,  4, or 9. Clue 13 also suggests that I is not 1, so I and Y are either 4 or 9. He proceeds in this way and soon can guess the first hint: BY ITSELF (?YI?????).

My messy calculations

With a few hiccups, he struggles to a full grid and completes what seems to be the hints: BY ITSELF, GAP RDX J NUM Z. What on earth can that mean? To a computer man, it sounds like code. We puzzle over it for too long then decide to simply ignore that strange string of letters and simply put all the numbers from the grid in ascending order and try multiplying them by themselves and inserting a GAP.

This task has fallen to me and I idly multiply the first number by itself (13 X 13 = 169) and put a gap into it, giving 16 9. Wasn’t this puzzle all about squares? It is perfectly obvious that if I take the square root of those two numbers, I get 4 3, remove the gap, and that gives another number that appears in my list – 43!

I try it with the next number in my list. 19 X 19 = 361. The square roots of 36 1 are 6 1. Remove the gap and yet another number from my list appears. Eureka! With a shout of glee, I tempt the other Numpty back (he has gone to bed by this time!) and we work our way through the list until only 1771 is left. That squares to 3136 441, which gives square roots of 56 21. That goes under the completed grid.

What a compilation! I hope Elap will give us a setter’s blog to tell us how long it took him to find numbers that would work and dovetail into a symmetrical grid, and why he didn’t tease us with some unlikely phrase made from the un-hinting letters,  RDXJNUMZ (which are used in clues) and CHKOVW (which are not). Perhaps in Welsh or Serbo Croat?

1. ### Alastair Cuthbertsonsaid

Hope you remembered to put in the 5621 as it’s not in your picture!!

2. ### shirleycurransaid

Pretty sure I put it in the one I sent.

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