Listener 4114 - Three Square by Elap

[Philoctetes]

No - I haven't quite finished it yet. Still, one of the joys of a Listener comes when you learn something new, and primitive triangles are new to me. I assume that the numbers in the threes are also the genuine "answers". I do love the mathematicals!

[JustinTime]

Mysterons,
As I understand it 2 of the 3 sides of the triangle can have a common factor provided that the 3 one does not have it.
So a 10:15:21 triangle would be OK a 6:8:10 would not.

[Ruthrobin]

No, the instructions seem to me to say that all three sides are different and all are primes.

[dr b]

I'm now where Andrew is (or was) and will put it down for a bit. I wish I could say I found some elegant way in and found a logical key that unlocked it all, but it's just been brute force and a lot of Excel. (Excel users probably have already discovered that the GCD function is useful for checking the relative primeness of two numbers.)

[AndrewG-S]

Still there dr b and will take my hat off to anyone who does this without excel. Just spent a while checking all my relative primes and all my answers are as Ruthrobin describes. I actually also have two solutions to my final entry in the grid...now back to those pesky shaded areas

[AndrewG-S]

Based on the cryptic preambles we have had recently you probably have to insert your thumb and forefinger into the shaded cells

[aldanna]

A week off for me, as I always pass the numericals to mathematician husband, though we send them in using my name, to avoid undue record keeping. Ironically, the only time I was ever listed as a Listener prize winner (runner-up) was one of these, and all I had done was offer a few thoughts on the end bit. Very spurious moment of glory! Never got the book, though, despite writing about it.

[AHearer]

Grey and empty -- that's my mind and those corner squares. I'll put it to one side and hope inspiration will come.

[Mysterons]

Thanks Andrew, I now realise that I was reading R5 down instead of across !! ... and that's after rechecking everything at least twice. Regarding the triangle sides RuthRobin, they need not be prime lengths, but they must only share 1 as a common factor.

[AndrewG-S]

I have doubled checked and still seem to have two alternatives for z2 and y3, anyone else have the same issue?

[BlackHugh]

Thanks to Excel I've also now finished the grid apart from the shaded bits. Although I'm a bit worried about AndrewG-S's mention of an alternative solution - I thought I had proceded logically and only got one solution hmm.

[oldvic]

Thank you in advance, guys, for not giving the game away...

Elap

[AndrewG-S]

Thank you in advance for an enjoyable puzzle Elap, I hope this doesn't eat away too much of my weekend. Clever construction so far.

[dr b]

andrew, I am pretty confident there's a unique z2 and y3; these were my last in.

[AHearer]

I got z2 and y2 a few steps before the end, with no ambiguity that I could detect. And thank you, Elap -- I'd better say that now than after lots more hours of failing to fill the corners, as then I might not be so grateful!

[IainGrace]

What a relief. No crossword this week - just a number puzzle - so we can concentrate on finishing 4113................

[dr b]

Still pondering the shaded areas, unsure of what to do based on the preamble: "ensure ALL rows and columns are thematically consistent." But what's the theme? 3's? Squares? Relative primes? Triangles? All of the above? I have been looking for a way in which the complete rows and columns are "thematic" to no avail.

Well, I am being dragged against my will to see the latest Harry Potter film (a Thanksgiving weekend tradition, I'm afraid). I stopped reading the books after #2 (when my kids could read the damn things themselves), so I have no idea what's going on; I slept through much of movie #6. Perhaps I can sneak 4114 and a penlight into the theater.......

[BlackHugh]

Dr b
I have been working on the assumption that the only useful clue to the theme was in the title, although I must admit that this hasn't helped me at all , so maybe that is in error.
Enjoy the film - my children, who went to see the film for the second time this evening, have reached the teenager stage of not wanting to be seen dead with a father in the cinema.

[AndrewG-S]

All done, nice puzzle thanks Elap.

[AHearer]

Well, dr b, I went to see the latest Harry Potter last night too -- and if you managed to sleep through it you must have been VERY tired or visiting a cinema with a broken sound system.

[AHearer]

Oh, and BlackHugh, my wide and I got taken to the film by my son and his girlfriend, mid-twenties, so there's light at the end of the tunnel (which is more than can be said for this puzzle).