# Posts Tagged ‘Bearskin’

## Listener No 4569: Bearskin by Elap

Posted by Dave Hennings on 13 Sep 2019

As usual with an Elap mathematical, I get a feeling of dread. That said, all mathematicals fill me with varying degrees of dread. Elap’s last gave us two 5×5 word squares. This time, we had four 4×4 squares, and it seemed they would be wordy as well, given that the digits had to be replaced “preferably all in upper case”.

The letters in clues stood for 27 different integers formed by taking a perfect cube up to five digits and truncating the first digit and any remaining leading zeros. In fact, they had to be “shaved off” and that, together with the title and 13ac’s r-A-Z-O+r would undoubtedly mean something!

As it turned out, this wasn’t too tricky a puzzle. Listing all the 5-digit primes, minus their first digits and zeros, gave 42 such numbers ranging from [2]7 (3³) through to [9]7336 (46³). After truncation, they were from [6]4 to [2]9791.

The starting point was 4through where UUU (3) was a 3-digit number and had to be 7³ = 343. 17dn (E – pp (3)) came next, with p = 4 and E = 331 or 375. Next was 8th (Uz – pp (3)) with a couple of options for z followed by 12ac (CU – UU (5)) where C had three options but, crossing with 17dn, gave 6656 as its value.

From there on, progress was fairly steady although not as quick as I initially thought it would be. It was nice to just have to rely on pencil, paper and a calculator. No doubt some out there decided that a program written in C#+ would be a good way to tackle it!

Sorting the values into numerical order, we ended up with pUzzLiNG (solvers’ activity in filling the grid), dEPIlaTORS (what replaced values 0–9) and A WorD CuBe (what solvers should end up with). The word cube that resulted had 4-letter words running across, down and through the cube.

Thanks for an enjoyable and easy-going mathematical, Elap.

## Bearskin by Elap

Posted by shirleycurran on 13 Sep 2019

Bearskin indeed! We really dislike the three-monthly numerical Listener puzzles so there was plenty of bear-like growling and gnashing of teeth from the other Numpty while I discreetly got out of the way and converted a massive bag of greengages to jam then prepared the supper. Yes, of course I had already hunted for traces of alcohol in those verbal clues and had discovered only a dubious B + ir – i – r. Pretty second-rate beer but cheers anyway, Elap.

The other Numpty’s comment was “Why so many letters in the clues, and why do we have some in both upper and lower case – in particular what was the need for a lower-case l that meant that it had to be specifically distinguished, in the pre-ramble (yes it was a bit of a ramble wasn’t it?) from upper case I?” and “That final clue to ‘pz + Z + L (3)’ must be a gentle joke – or does it have a meaning?”

Clearly it did. After solving U and C the growling began and lasted for hours.

It is only in retrospect that I have wondered how Elap managed to create this puzzle and surmised that he must have struggled initially to create four word squares using only ten letters that could be converted to the digits 0 to 9 (and leaving letters to give ‘A WORD CUBE’ and ‘PUZZLING’) without using any letter more than twice. No wonder he needed that preambular clarification of the lower case l.

With a table of cubes of integers to 100 in Adrian Jenkins’ Number File (you can obtain second-hand copies on the Internet) we constructed a list of potential digits and were ‘puzzling’ from then on for rather a long time, but it was the guess that the first word (‘Sorted by numeric value’) was pUZzLiNG that finally got the Numpty Bear moving forward dramatically rather than sharpening claws (and pencils).

The ‘throughs’ helped us by providing intersecting digits and after many hours of working from letters we had to letters we needed, three of the four layers were completed but we could see no way to produce numeric equivalents for d O u A R and P and fill that bottom layer. It was well after midnight that we decided to place the letters we had in numeric order and that produced:

pUZzLiNG EILaTRS A WorD CBe.

Penny drop moment at last. The final three words were A WORD CUBE and we could place the remaining d P and O to give DEPILATORS. Ha! So that explained the “Bearskin” heard as BARE SKIN.

Finally there was a smile from the Numpty Bear and as it was by now well after midnight, we jointly converted those nine digits to DEPILATORS and produced our WORD CUBE. What was most astonishing was that it didn’t just have real words on all four layers, going aross and down, but also that the through words were all real too. What a fine and challenging compilation.

(Did I say that? I hate the things and am breathing a sigh of relief that it’s three months until the next one and last one of the Listener year.)