This week, a puzzle from one of the small band of mathematical setters. Two years ago, he presented us with a triangular grid and triangular cells and a proliferation of triangular numbers. This week, a nice square grid with square cells.

Reading the preamble, however, we had MP, DP and DS numbers to calculate. MP was Multiplicative Persistence — try saying that after four pints! Checking in with Wolfram Alpha, I found that it wasn’t just something that Oyler had made up. Similarly, the two lists of numbers, Happy numbers and Lucky numbers, also had a mathematical derivation which, thankfully, Oyler didn’t spell out as he’d have run out of space.

As is my wont, I’ll refrain from a detailed run-through of my solving, but starting at 2dn *Palindrome and multiple of 5 with MP of 2* (3), I got 5-5 which led to 1ac *Triangular number with a triangular DP* (3) being 153, 253 or 351. 23ac *Palindromic prime* (2) had to be 11 and from 11ac *DS equals 21dn* (4), 21dn had to be 10, 20 or 30 since 11ac was -5– and therefore a maximum DS of 32. Well, that was all the easy bits!

It should have struck me at some point before the endgame that almost all the entries had at least two alternatives, but heigh-ho it didn’t (and I’m not sure how much it would’ve helped anyway). Fast forwarding to the end, we had to use an innovative coding technique — 1 = A/K/U, 2 = B/I/V, etc. I nearly overlooked a little statement where I had “If 1dn = 12” and led to the instruction (7,6,7) being utter gobbledygook. Luckily I noticed that before going back to square one and 1dn = 38 gave me **Reverse across entries**.

Thanks for an entertaining and fascinating puzzle, Oyler.