Number Plates by Xanthippe
Posted by shirleycurran on 9 March 2012
This must have been the quickest numpty pdm ever. The mathematical numpty took one look at the preamble and said, ‘They are probably US states zip-codes. After all, there can’t be many other sets of fifty two-letter items (adding together the 38 and the twelve that were to appear down the centre columns).” So why am I writing this blog almost twenty-four hours later? That ‘ambiguity – there was the rub!
There was a long didgetty slog with about twenty pages of calculations appearing and two backtracks, when the grid fill that was slowly appearing suddenly didn’t work any longer. I did a bit of housework, talked to the kitten and studiously steered clear of the blue air. He doesn’t like the tri-monthly numerical Listener any more than I do though he performs better on them.
What a pleasure though to see that there were some words involved in this one. Now and again I crept into firing range and we managed to fit in LAV or LOO, RAI, ILL, DZO and CRU. These would, of course, help us later when we had the complete set of 12 (SPY, FAN, OWT, GAM, ADD NEW and JAY in addition). Good to see, too, that even in a numerical Xanthippe managed to uphold the Listener compiler tradition of a healthy tipple with his CRU!)
Meanwhile, Numpty No 2 struggled with the maths wondering whether he had started at the right place. How restrictive were the clues ‘sum of digits = 10′ and ‘sum of digits is prime’? Was this the place to look? In fact, only 6% of three-digit numbers and about 3% of four-digit numbers have SD = 10. Helpful but not terribly! For the prime sum, it is about 3% for two-, three- and four-digit numbers. So neither of these clue types was strict enough to be the starting point.
a, n and r were the place to start, and, as usual, there was a long grind with several arithmetical errors causing frustrating back-tracking. That’s what we dislike about the numerical three-monthly battle. Unlike the verbal ones, there is no slow onward satisfaction. Discovering a new number (except perhaps for Ramanujan’s number plate) doesn’t always carry with it the joy that comes with clever verbal manipulations. It is just a number.
However, Saturday morning saw a full grid and the penny had clanged to the floor hours before, so we were left with the task of working out that series of digit choices presented by the number plates in the preamble and using the numerical equivalents of states to eliminate, one by one, the 50 official ones. 50, we had been told, so we forgot about DC (having established on the Internet that it is not an official state).
Of course, all went well. There was only one AZ, one TX, one SC etc and ambiguities disappeared when we used the numbers in the central column. Until … we were left with three 21s. Consternation! We needed to eliminate New Mexico, North Carolina and NEW YORK! But according to our reckoning, New York had to be 22.
The culprit had to be that second square of the seventh column, since any other resolution of the problem would leave ambiguity. But we couldn’t simply wipe out a computed result and put 2209 in the place of 2109 as the result of 127n – SQRT(2(x – u)) could we?
That’s why I am writing this blog almost twenty-four hours after we started our solve – when I ought to be cooking dinner! It has taken so long for the other penny to clang to the floor. I am told there has been this sort of devious playing with square roots before. A square root can be a plus or a minus quantity. (Is that honestly part of ordinary level mathematics? I am also told that these numerical puzzles should be within the skills of anyone with ordinary level basic mathematical skills. Hmmmmm! It is this sort of thing that makes me dread the number jumblies!)
So 2209 went into that slot and neatly converted to New York (alongside Arkansas or West Virginia – we didn’t have to decide which did we, as that stayed as digits).
OK If I mange to moan for a few more weeks, I’ll earn a reputation as the Whingey blogger so I had better say how we admired the brilliance of fitting all these states into the grid and that, in fact, apart from that stinky little trick at the end, this was fair and verging on enjoyable, so thank you Xanthippe.