Listener 4464 The Properties Of Numbers Ii By Piccadilly

[Contrarian]

Absolutely incredible feat to make the set of statements apply both to the numbers and their associated entries.

Unfortunately for me, though, I can't see a solution. Having reached an impasse, I backtracked, checked my working, but just can't find the error.

Hats off to the successful solvers of this one.

[jim360]

A fairly trivial problem in the end, although I use "trivial" in the same way that it's "trivial" to solve quartic equations.

Nice that there is a "final" clue, in some sense, that relies on everything else being right, so that this puzzle is very much self-checking, but I did find poring over multiples of 7ac and possible squares that intersected with the 3rd digits of four-digit cubes a little too close to tedious.

[Ruthrobin]

The first four and a half answers only took about an hour then it really slowed down. Oh for an easily searchable table for five-digit primes rather than bodging about to make such a table as we had to do and faffing around with pencil and calculator. It is a relief to be done with it. Thanks anyway to Piccadilly.

[emcee]

Really enjoyed this; several multi-layered "mini puzzles" meant it wasn't going to be dashed off as quickly as some.

I am ever impressed by the construction of these types of puzzle. To me, the clever people are the compilers rather than the solvers of such puzzles.

Many thanks, Piccadilly.

[Cloverjo]

Oh lovely, a numerical. I'm not being sarcastic, I do love them. I haven't looked at it yet, but looking forward to it.

[12barblues]

As with some of the others this resolved into several mini-puzzles and unlike some other numerical they didn't seem to get much easier. The use of digit sums, at least to this extent, also seemed novel to me, so lots to admire.

[Encota]

I loved this one: a quite brilliant construction with all statements working on two levels. I've only ever seen two puzzles remotely like this one - it is superb! Thanks Piccadilly! Best get on with writing & scheduling my blog on it at LWO whilst it is still fresh :-)

[Oyler]

23 years after the original which in my opinion is the best ever Listener numerical we get the sequel. Well worth waiting for and I hope we don't have to wait another 23 years. Superb puzzle. Thanks Piccadilly. I presume I'd better make a start on setting Casting out Nines II and hope it appears in 2020!!

[Cruncher]

Quite enjoying the slog of this but making grudgingly slow progress and am struggling to find elegant steps and handholds

[midgler]

Beyond me, although I can't help noting that the much discussed forum conventions seem to be more loosely applied to numericals! Somehow a copy of Chambers seems a curious prize.....

[fyellin]

Usually, numerics become tedious after the first few "aha"s. "Okay, what are the multiples of 591 that fit this pattern", over and over again.

This one was extraordinary. Problem solving and real deductions all the way to the end. Very little just looking for the answer that fits the pattern.

Definitely the best numeric in a long time.

[Ruthrobin]

Yes, Midgler (and good to see that you are still with us). I think a few of us have made the comment before that one would hardly be doing Listener crosswords if one didn't already have a Chambers. However, should you win (statistics seem to operate and some people win several times and some of us never) you can ask the editors for a list and they will offer you two or three other books that are available as alternative prizes.

[Cruncher]

Glad it all worked out first time. Not sure I would have had the patience to unpick it. My 5km Parkrun this morning was a lot easier

[Contrarian]

After another assault on the puzzle this morning, I managed to see where I had gone wrong previously.

Quite incredible the way that what appeared to be very minimal information about the digit sums of some of the entries provided just enough for a unique solution.

[olichant]

I admit I just checked in here to see if anyone was struggling as much as I am. I'll duck back out again - am just being a bit slow.

[borealis]

Help, please - not with the answers! I've been away, dont have an electronic subscription and have missed the last two weeks of Saturday Times. Would any of you be kind enough to forward me 4463 and 4464, please? I'm at bo21realis at gmail dot com. Thanks!

[borealis]

Have both now; thank you!

[olichant]

I found that seriously tough, compounded by some (admittedly stupid) errors of my own making, with all the back-tracking thereby incurred.

The construction is obviously very impressive, and the self-reference is a neat idea. I found it more of a slog than fun, but I suspect I didn't approach it cleverly enough.

[Philoctetes]

Just finished, and thought it was the perfect numerical. Apart from appreciating the skill of the construction, it was mostly a logical exercise of fitting together apparently unconnected or even random bits of information. There was a logical path. I did use a spreadsheet, but not for abstruse calculations so much as listing and eliminating alternatives. (Btw, Ruthrobin, I can recommend building up a spreadsheet of all the different number types we encounter in our quarterly ice-bath. Mine now has well over 20 tabs)

[icynorth]

I had the Olichant experience - but I had to backtrack no less than 5 times. I then committed the spreadsheet to digital oblivion (apart from a list of primes) and started on it logically from first principles. I how have a 112-step derivation of the unique answer (which is impressive), but two of the inequality clues turned out to be redundant, sadly.

It didn't teach me anything, but I agree it's an excellent puzzle of its type. Thanks, Piccadilly!

[borealis]

icynorth, I wish I had your dedication. I probably had about 112 steps, but only had one redundant clue (not an inequality). I find it very difficult to record logical deductions while I'm following them. Magnificent puzzle, lots of logic and very little number-list staring. In awe of some of the construction. Great stuff, Piccadilly.