## Listener 4151 Ruslan’s Nummer or Number (as in Make Numb)

Posted by Dave Hennings on 9 Sep 2011

Our three-monthly journey into the mathematical world of numbers seemed, this week, to be into the mathematical world of letters! Ruslan’s third mathematical Listener required that we enter the initial letters of the digits (O, T, T, etc), rather than the digits themselves. Not only that, we had to get our heads round the German equivalents as well (E, Z, D, etc). And then we had to put ourselves into the head of this *dummkopf*** solver who couldn’t separate the two languages!

It sounded easy-ish, although I think I read the preamble about six times before I realised that what seemed a fairly obvious job was “doin’ my head in”!! Were the answers to the clues the same for both puzzles, with two letter-equivalent puzzles being different, or could the whole thing be different for the right-hand grid, with different answers and different letter-equivalents. I decided to solve the left-hand puzzle first and see what transpired.

After 20 minutes, all I had was that 21ac began with a 3 or a 4 … and I’d been given that by the T in the grid. 30 minutes later, my brain still hurt; I was totally stumped. It seemed likely that the entry-point would be in the bottom right corner. The last letter of 24ac D^{2} was the same as the last letter of 19dn A^{2}, and 21ac ABI and 15dn BD^{2} intersected, but there seemed to be too many possibilities.

From 17dn *2(2I-B-Z)(I-D)*, I was pretty certain that I > D. However, what about 6dn: *D+A+Z+I ^{2}-(F+T)(D-A-Z)*? Could I rely on (D-A-Z) being positive and that D > A and D > Z or could the subtraction be of a negative number to give an addition:

*D+A+Z+I*? (Remember 1ac in Arden’s Square-bashing last year?) I naughtily made the decision to treat D as the largest of the three numbers.

^{2}+(F+T)(A+Z-D)After about 15 minutes, I realised that, although there seemed to be a lot of possibilities ahead that needed calculating, I had to plough on. In fact, it wasn’t *quite* as daunting as I had thought. However, a self-induced trap nearly derailed me before I realised my error: even though I had been told by the preamble what the spellings of the 10 digits were in German, I had been using F for Fünf and for Vier (**)! I mean, fancy having two letters give the same sound! Was it just in German? It certainly seemed unlikely! I made a list of number-letter combinations which I had originally thought superfluous, making sure also that the German for 2 gave Z, not D like the romantic European languages.

Plain sailing comes nowhere near describing my progress on this puzzle, but miraculously I got there in the end. Well, I got to the end of the left-hand grid. Looking to see what the English equivalents of the German entries was, I found **Footnote: Nonsense** soon enough, indicating that the “*adapted from a version in a German newspaper*“, as stated in the preamble, wasn’t true. Well I guessed as much, so back to the right-hand grid.

It was soon evident that 21ac could not just be a different encoding of the same answer since it led to anomolies fairly quickly in that corner. It was back to the drawing board, and I took pretty much the same route as first time, but without restricting 21ac to 2••• or 3•••, and without assuming that D was larger than A in 6dn. As with many mathematical Listeners, I expected to find a mistake in a calculation as every entry was slotted into the grid, but amazingly, everything went well on the second puzzle and it was completed just as my stopwatch read 5 hours! A long time then, but nowhere near as long as some other recent mathematical puzzles.

A fascinating idea from Ruslan that caused me quite a few headaches, and I was glad to get there in the end. I’ll make sure I have a supply of Ibuprofen® before I start on Ruslan’s next puzzle.

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