“Alma Mater”, said the other Numpty. ” Quite a coïncidence as 2013 is the 600th anniversary of my first Alma Mater, St Andrew’s University. Well, down to work. Let’s work out the frequency of those letters. Hmmm! Strange, there are only 8 letters used. D, T, E, A, W, R, S, N!”
I hadn’t yet retreated out of firing range (as I habitually do until the later stages of the numerical Listeners – which can be several days of bearish growling later) and a minute’s fiddling with those letters provoked some muttering: “More than a coïncidence here. St Andrew’s! 1413 to 2013! This Saturday is also St Andrew’s day. Well done, Oyler! Preamble understood, perhaps? Do you suppose we put those two dates into 1ac and 31ac? That seems more than likely, and 1d can only be 1xx, so 1ac is 1413 and, 31ac is 2013. Progress! And the thematic shape must be a saltire, roughly corners to corners, passing centres of squares containing 1,4,1,3 and 2,0,1,3.” (Three minutes into a numerical Listener and the theme sussed – that has to be our record!)
Arithmetic might now be needed. A list of prime numbers is opened and there are only 21 from 11 to 97. Eight have to add up to 600 to thematically commemorate that anniversary. Some clues are numbers like perhaps 73^71. Awkward. I doubt that we have the calculator or device to work that out, but since Oyler is apparently a St Andrews man it’s probably not necessary to do a lot of maths, just find a shortcut to get the last digit …..
To sum to 600, these 8 2-digit primes are likely to be the forms x1, x1, x3, x3, x7, x7, x9 and x9, so the 8 tens parts need to add to 580. No 1x is possible, as the maximum for the 7 others is 559. Neither is 2x or 3x. That leaves only 13 primes to choose from ranging from 41 to 97. Looking at 18ac, 600+D-W-2E, this can only start with 6, 5, 4 or 3 so A can only be 71 or 79. Guess 71? From 23ac, S, and 15d, AS, needing a common last digit, S must end in 1, so is 41 or 61. So is Oyler being kind, with S,T,A,N,D,R,E,W in increasing order, as 41, 67, 71, 73, 79, 83, 89, 97? Looks good! Digits interlock! Even the splendid WANT+REDS, DREW+STAN and SWAT+NERD fall into place.
What about 10ac, N^A or 73^71, and its friends, 2d, 3d and 20d, the giant numbers? No problem really, as 73*73 ends in 9. So 73^4 ends in 1, as does 73^68. So 10ac ends in last digit of 73*73*73 or 7. The others can be handled similarly. What an ingenious and pleasant puzzle, no computer needed, only fingers! I admit that the literary Numpty spotted the saltire-defining squares first, though.
It had to be he saltire didn’t it – especially considering the shape of the grid (unlike that Swiss flag we had a few years back, that used one of the very rare square flag shapes). It was obviously a matter of searching along the diagonals, and, sure enough, there on the 1st, 3rd, 7th and 10th were the culprits. Saltire it is! Thank you Oyler for our speediest and most enjoyable numerical Listener ever!