Listener Crossword No 4595 Equality By Elap

[icynorth]

Am I the first?

I’m simply astounded by the result. Number theory is just an amazing thing to delve - thanks Elap.

And a decent pen/paper/calculator one, too! Although my final checking was reliant on the first 8 significant figures being correct.

[Scorpius]

Certainly an amazing result.

This was far more straightward than a cursory scan of the preamble suggested. I actually enjoyed it, which is more than I can say for some of the more complex number puzzles.

Thanks, Elap

[Cloverjo]

I love the number puzzles. I think a little too much wine had been taken when I attempted it last night. I’ll try again today. I’m looking forward to the end result.

[Cruncher]

Halfway stage with a completed grid. And time for a lie-down in a dark room before I embark on the next bit...

[perseverer]

I have mixed feelings about these numerical Listeners. I made rather heavy weather of the grid fill here, so I am not sure I can really say that I enjoyed that aspect. However for me the pleasure comes from the satisfaction of getting to completion, and from marvelling at how the setter is aware of the property in the first place and manages to construct the puzzle to show it.

[emcee]

One of Elap's easier ones but, nevertheless, most enjoyable.

An incredible property held by NINE sets of six numbers. Elap, how on earth did you light on this result?

Thanks to Elap for another great numerical.

[sunny-dave]

I don't like numericals - they may have been my initial interest in Listenering, but those days are long gone & now they are a chore which I usually give a swerve to ...

... but ...

... I was at a loose end yesterday afternoon, as the Kerry rain lashed down, and so I had a 'bit of a look'.

Glad I did - a decent challenge of a gridfill (doable without deploying any heavyweight artificial aids), and then a fascinating property revealed in the endgame.

Thanks Elap - an excellent puzzle.

[Philoctetes]

Just finished. I enjoyed the initial gridfill, pondered the second stage, did the calculations and.....
One of the sets just would not fit. My ultimate nightmare is getting to the end of a numerical that seemed perfect until the last piece would not fit. Eventually I found that I had written the equivalent of one of the letters wrong by 1 - used the correct value when approaching the clues mentally, but used the written value when I had used pencil and paper (just once).

[Oyler]

Very nice puzzle based on one from 1957. Thanks Elap

[borealis]

Very nice. Straightforward but enjoyable, and like Philoctetes
I ended up with one digit wrong.

[BMACMAC]

I was busy over the weekend, and only had time to get started on this yesterday. I was relieved to find the grid fill much easier than some recent numerical puzzles and was amazed by the final result, like most others judging by other posts in this thread. Thanks, Elap, a delightfully constructed puzzle. Just one slight worry, concerning the minimum value of N. Nothing in the preamble or hint says that N cannot by zero or negative. To a non-mathematician, the notion of raising a number to a zero or negative power could be hard to fathom, although mathematicians use the equation (x^m)*(x^n)=x^(m+n) to give definitions: x^0=1 and X^-n=1/(x^n). Suing this one could argue that the property is true for N=0, which it would be for any set of six positive integers. I wasn't sure whether or not this would affect the "correctness" of an solution submitted that ignore this.

[BMACMAC]

icynorth: in reference to your final sentence regarding calculator accuracy, it is often the case that calculators store far more than they can display. If you can store a result in memory, then arrive at another result which looks the same, you can usually do -MR to subtract the first result from the second. If you get 0, then the two values are equal at least as far as the accuracy of your calculator's stored values are concerned, which would normally be better than just relying on what has been displayed.

[logophile]

The preamble makes no reference to N always being positive so its lowest possible value has to be zero.