Listener 4256 - Boxes By Radix

[olichant]

Oh my goodness.

What an incredible feat from Radix. I have not been able to put this down since I got a foothold in - the construction, symmetry and elegance make the mind boggle. I am slightly ashamed that I used a late-twentieth-century technique to make headway, and (for the moment) I cannot imagine how I could have completed it otherwise.

Truly humbling. Thanks, Radix. I think I can now understand what people see in numericals!

[jim360]

Well, yesterday wasn't entirely wasted. I now know the 31 primitive Pythagorean quadruplets with d = 261 and all of a, b, c greater than 23...

[JustinTime]

Oh Really !
I thought it was (like most/all numerics) a complete waste of space.
As I have said before, with a proper wordy crossword one usually learns something vaguely useful (in a bizarre set of circumstances), here no such animal emerges.
No, not even elegant because it required the additional word to resolve 'apparent' ambiguities in the grid.

[freiheid]

Thanks Radix, I needed a weekend off!

[emcee]

The first ever Listener numerical that I have needed to write a program for. Not impressed.

[dylan123]

I cannot see any way of solving this puzzle without a computer and a programming facility, such as Basic. This seems unreasonable

[jim360]

The morning has yielded much better progress. Hopefully... still not sure what will come of the "c integers" message.

Don't think a computer program is needed, but it sure helps! Excel for the calculations, which is just a faster calculator.

[Philoctetes]

Current (slow) progress is perfectly feasible with a simple calculator, pencil and (lots of) paper. Might move on to spreadsheet soon, though.

[IainGrace]

Nothing we have read here encourages us to spend time on this, which is just as well as we are behind the pace with last week's, having been away.

[captaincoma]

You must be joking. Life's too short.

[Texasetes]

I wonder whether JEG will be bothering with this.

[dr b]

Of course, a masterpiece of construction, etc etc, but:

Having read some about Pythagorean quadruples, there does not seem to be a shortcut way in (I'd love to hear if I'm wrong), so:

No pdms, it's immediately clear what needs to be done, so:

pencil & paper would be tedious beyond belief (just converting integers to letters in base 24 by hand would drive me nuts), so:

out comes the spreadsheet; write a function to convert answers to base 24 letters, write a program to find quadruples that meet all the constraints, and:

this just becomes an exercise in brute force, with a bit of logic thrown in as crossing entries put further constraints on an answer, so:

not my favorite numerical. qed.

[lyrabelacqua]

As Niles Crane said of dancing, "This is boring yet difficult..."

[jockie]

I've not spent more than an hour or so on this, so perhaps it's too early to say I'm beat. But others have observed that sheer tedious number-crunching seems to be required. And that the volume (if not the complexity) of this seems to require some sort of computing power, even fairly low level. (I don't regard a calculator as "computing power" in this context.) A normal Listener puzzle requires the solver to go through all the clues, and usually at first read several can be worked out (and even inserted if it's not a Carte Blanche), thus providing assistance at the next stage. But numericals don't usually do this, and the clever part for the solver is working out where the "way in" is likely to be. Like jim360 I have a maths degree from the same ancient university (although sufficiently long ago for my brain to have begun to rust) but for the life of me I can't see the "way in". I have a sneaky feeling that this puzzle was like the prime number thing where it's fantastically simple to multiply two 10-digit primes but fantastically difficult to factorize the product. Naturally if I'm wrong I will take my hat off to Roddy - indeed, I do so already as it's clearly a masterful piece of construction.

Word-based Listeners can be solved with a pencil and the BRB (and occasionally another reference book like Brewer or ODQ); numericals should surely not require more than the arithmetical equivalent - a pencil, a calculator and perhaps a list of prime numbers. But I shall struggle on .... (way in guide welcome though).

[Cloverjo]

I agree, jockie. I thought there must be a way in, from which everything else would gradually unfold. I also wrote a little program in order to speed up the discovery of "the way in", but there seems to be none, just lots of number crunching. However, I do enjoy the numerical puzzles and am intrigued by what the word and the apparent ambiguity might be, so will crack on. Enjoying it in my own way.

[Cagey]

I am a medic, with no maths degree. There is a way into this puzzle that involves only a little brute force, that can be done on a calculator. Email stuartc.thomas at nhs dot net if you want nudge. I think the puzzle is fair.
Stu

[starwalker]

Z cup +

[PureListener]

I could see no obvious starting point so I wrote a program to calculate all possibel clue answers. Then it was fairly straightforward and took about an hour to complete. By writing a computer program to effectively solve the crossword, have I cheated? Having seen all possible clue answers (32 pages of single column 8-point font), I can't see how anybody would be able to complete this, especially with the complication of converting to and from base 24. A masterly construction but I am sure most solvers did not even bother to start.

[lyrabelacqua]

Finally finished, thanks to a helpful nudge from Cagey. You do not need to write a program, but Wincalc (which has a built in feature to produce the sets of numbers you are seeking) will speed your progress. I cannot say I really enjoyed it, but I am enjoying having finished it. The construction is impressive, but the experience was a little dry for me.

What does Z-cup mean?, and why do people (unhelpfully) keep using it as a comment?

[dr b]

The Z(abadak) Cup is named for someone who doesn't post much any more but often had the grumpiest reaction to the week's puzzle. A joke that is so "inside" it cannot be perceived without an MRI scan.

It reminds me of the old old joke:

A group of salesmen who frequently traveled by train together had heard each others jokes and stories so often than they began to refer to them by numbers rather than retell them again and again. A young salesman new to the group listened to the banter for a while - "remember #22 - ha!" and thought he'd join in, so he blurted out, "Number 16" and was met with deafening silence. He later asked a veteran why, and got the reply, "well, you told it all wrong."

[Contrarian]

Tedious, perhaps, but oddly satisfying.

Just to add to some of the comments already made, I fail to see you this was possible without the aid of a computer program. For the clues involving 4 base-24 digits, my program took a couple of minutes to calculate the list of possible a/b/c triples satisfying the initial conditions. I dread to think how one long it would have taken with just a calculator or spreadsheet.