Listener 4386

[crosswhit99]

Quite an appropriate puzzle given the weather we have been having this week ! Relieved that it didn't take too long to crack as we have the pleasure of another Schadenfreude puzzle to occupy us tomorrow. Many thanks Elap !

[fyellin]

Sigh. I spent too much timing using the wrong secret decoder ring. (And failing.)

[olichant]

Took me ages to figure out the decoding, but we'll worth it in the end. So neat the way it all falls together - a really nice multilayered numerical. Thanks, Elap.

I think I found a neat proof of the hailstone conjecture, but the answerbank answer box is too small to contain it. Shame...

[Elap]

Thank you, olichant. I'm glad you enjoyed it.

The last part of your comment is very appropriate because I'm currently reading Simon Singh's Fermat's Last Theorem!

[Oyler]

Neat puzzle that used the same theme as Arden's Eureka that appeared in The Magpie issue 141 in September 2014.

[Elap]

Coincidences like this will always happen - this puzzle was submitted a year earlier than that...

[sunny-dave]

Thanks Elap - a great numerical I think.

The gridfill was (for me) what numericals should be - a Goldilocks problem. Just hard enough not to be trivial and just easy enough to doable without deploying any over-the-top coding and/or spreadsheeting resources.

The message was tricky, but fair, and then the eventual gridfill was easy enough. All in all a nice challenge for an inclement weekend.

Mostly, though, I'm in awe of the ability to construct this - two grids, both uniquely solvable and just enough commonality for it all to work - very clever indeed.

Thanks again

Dave

[Ruthrobin]

Elap, you know we would love a setter's blog on Listen With Others. Please!

[Elap]

I've already prepared a setter's blog which will appear in LWO.

[Oyler]

Elap as you say these things happen and it is fun to see the different take you took on the theme. Numericals get published quicker in The Magpie of course as they have three times as many slots.

[Pasquin]

Thanks, Elap, a very nice puzzle. I stared at the grid for ages before noticing something, then the way forward became clear. When I've solved a numerical, I always like to go through it again, to see if there's a more elegant solution than my first attempt, and the path through this one was very tidy, with no backtracking from blind alleys, but great fun. And it's amazing what you learn from doing crosswords like the Listener.

[Oyler]

It may be of interest to some that since 2000 when we've had 16 numerical puzzles a year either in The Listener and Tough Crosswords or The Listener and The Magpie those puzzles have been set by 40 different setters. Of those 16 have set only one puzzle, seven have set two and three have set three. Of the 14 remaining that have set more than three puzzles unfortunately only half of them are still active. So to those who have set only a couple please set more and if you are thinking about becoming a setter of numerical puzzles then go for it. I am always happy to give advice and help to new setters as are my fellow crucinumerists.

[s_pugh]

As an avowed loather of numericals and a maths dunce I was chuffed with myself to work out the initial grid (with considerable thanks to Excel).

Since then I’ve been utterly stumped with the next phase, despite trying every encoding possibility I can think of. There is simply not enough guidance to go on. It takes ambiguity to a hitherto unseen level.

This puzzle has done me the great favour of saving me countless future hours of wasted time and money, so thanks to Elap for that, but you’ve also lost a Listener fan.

[sunny-dave]

I can email you a hint if you would like, s_pugh ?

[email protected]

[s_pugh]

…. and of course no sooner than I put pen to paper than it dawned (albeit thanks to confirmation in ‘the other place’) of something I’d spotted earlier.

I still can’t imagine attempting this without Excel or similar, or maybe that just reveals my inability to apply mathematical logic. Thank god it was raining all day.

Thanks sunny_dave, got there before I saw your post!

[fyellin]

s_pugh: I think that except for the very last step, this puzzle was reasonable to solve without Excel. Typically I write code to solve numerics, and this one didn't involve anything other than a calculator.

Even though it took me way too long to find it, I knew exactly what the message was going to be telling me to do, from the very beginning. I was just missing one crucial piece of information. . . .

[Oyler]

This puzzle doesn't require the use of a spreadsheet at all. It can be done with a standard scientific calculator or just paper and pencil in a couple of hours. Elap did the hard work so you didn't have to!! Thanks Elap.

[Scorpius]

I started this very late, so have only just filled the grid. I can confirm what Oyler says, that Excel is totally unnecessary, and its use would have slowed me down considerably. Once you get started you just follow a logical path to the end.
I've yet to tackle the endgame.

I did make the mistake of initially writing down the first thirty hailstone sequences, thinking that might be a help but it was totally unnecessary. Then over coffee, just out of interest, I started the sequence for 31. Whereas each of the first thirty sequences took up less than one line of numbers, with 31 I gave up after I had eight lines of numbers where the general trend was ever higher. I've no idea how long it would take to reach a number that is a power of 2.

[Postigod]

Wow. Once I had stopped being stupid and found the message, this all came together beautifully. A great Listener and I can't wait to read the setter's blog.

My only tiny gripe (in fact it's not really fair to call it a gripe!) is that I can think of a 'more thematic' way of fitting the message into the grid - I was so convinced it had to be that way that it held me up for far too long.

[perseverer]

Scorpius Using this calculator the answer appears to be 106 steps.

http://www.mathcelebrity.com/collatz.php?num=31&pl=Show+Collatz+Conjecture

[Postigod]

Scorpius - are you sure that's right? If Wikipedia is to be believed, the number of iterations for a starting point of 27 should be greater than the number for 31 (both have a 'stopping distance' of a little over 100).