# Listen With Others

• ## Who Are You?

Posted by shirleycurran on 13 September 2013

The quarterly numerical puzzles cause havoc in the Numpty household as one Numpty is a double Numpty where Listener numerical crosswords are concerned, and the other one has all the solving to do. There is the occasional exception when the crossword might – just might – be considered to be within the range of a reasonably competent ordinary-level mathematician (as Listener wallahs claim they always are, ha ha!) However, that was certainly not the case with Radix’s Boxes. The first puzzle was attempting to understand the preamble. I got well out of range for a full day then dared to ask for a solver’s blog.  Here’s what the math Numpty said.

“I can only admire this remarkable construction, having finished the puzzle. However, … that little word … did anyone really solve this who could not write programmes to do it, or who is not a far greater expert at Excel than I am? I cannot believe it (but if somebody did, or found a magic method, I applaud with vigour!) I must also applaud the astonishing ingenuity that has gone into such a complex construction. At first, I struggled with what seemed to me to be impossibly vast sets of a,b,c values.

Use of base 24 gives the letters that then provide that subtly ‘hidden instruction’ but were difficult for the ordinary Joe to handle. Even programs proved to be very demanding when both strings and numbers needed to be manipulated. Our household calculators were not capable of the precision required (32 bit integers etc.) and I needed to download a freeware programming support system (Thin Air Basic) and re-learn it. The puzzle crumbled quite fast thereafter, with K and M, for example, offering a unique a,b,c, and E, V and L offering 4, 6 and 7 solutions. Sufficient to start a jigsaw fill with not too many ‘alternative pieces’.

How was I going to find that word that was to be written below the grid? We were told that ‘The 24 integers c (the heights) should finally lead solvers to the thematic word that must be written below the grid, thereby serving to resolve any apparent ambiguity. We should have read this more carefully from the start (isn’t that always the case with preambles?). We know Radix will never waste a word. ‘Finally‘! Finally, we read those final letters and what did we find? TOTAL HEIGHT IN BASE TWO FOUR. We had two ‘ambiguities’ A/M and B/Q. This meant that there were four calculations of the total height (by adding all the heights together) and when I reconverted those figures to base 24 and letters, two possible words of the four appeared. I had CAME and CASE. Boxes? Clearly, I had to opt for CASE:

Indeed, there is no doubt that this was a truly brilliant compilation and I have to applaud Radix  even if this led to even more Numpty head-scratching, cursing and program mistakes than usual. There were none of the habitual Listener tipples in this one (well, perhaps there were, was Radix producing not one but a whole CASE full of bottles?) On the stregth of that suspicion, we decided to have one anyway to toast a compiler who can produce challenging and flawless verbal crosswords and numerical ones too.

1. ### Jaguarsaid

This was most definitely the toughest numerical puzzle I’ve ever completed. I really hope there is a setter’s blog providing some idea of an intended solution. For me, and presumably for many, it felt rather like stumbling a vast thicket of numbers before stumbling on the right answer… I am in awe of the construction, and even of the very idea to put together such a puzzle.

2. ### Alastair Cuthbertsonsaid

It’s a shame when a mathematical like this appears as there is nothing for numerophobes to do!! Oyler

3. ### Antosaid

Yes, I resorted to writing a script to working out all possible solutions for each clue. I then dumped this in Excel so I could filter my results and then, starting with those where there was only one solution I was able to largely get this done by eliminating solutions that wouldn’t fit in the grid.

Was it cheating to use a script? Possibly, but it was a great exercise trying to get the script to be as efficient as possible, not to mention very satisfying to see that the solutions it provided were correct!

I wouldn’t have stood a chance without it!

4. ### Jaguarsaid

The Listener’s own website provides a fully-worked solution. I see now that the intention was undoubtedly to have solvers learn base-24 arithmetic, what with that handy “all odd squares end in A or I” trick, plus a few others. Most of my working was in base 10 — which is probably why I found it so hard. Oh well.

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