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!

[BlackHugh]

perserverer
Fortunately the T-Shirt codes had nothing to do with it and I found Google no help at all!

[Philoctetes]

OK - submission date is now gone, so I can ask a direct question. How on earth were solvers meant to find the theme if they did not have internet access? The numbers are not instantly recognisable as being part of a sequence, and it is unlikely that you could stumble across the theme by chance.

[BlackHugh]

Well - I did get those numbers without using the internet (although as I said above I tried and failed to get them through Google). I do, however, have a degree in maths so I was familiar with them and the formula for generating them. Without that I think one would struggle.

[JackDeCrow]

Having tried googling some of the numbers themselves early on, with no success, it was only several days later when thinking "what is the actual theme here?" that it occured to me to look up whether there was such a thing as a "triangular number". Naturally, I did use the internet, but I guess that is something one could have looked up in a library as well and dicovered the formula.

[Jogler]

I have very rusty (and very ancient) O level maths. My other half (the h-g) is much better versed in these arcane arts. We had a good idea of the theme from looking up the title in the BRB and extrapolating from there. We did not get any further help by googling. We didn't think that it necessarily followed on terribly smoothly.

I had successfully followed the number work up to this last step and I am a little disappointed that it was beyond my abilities to do the last bit as I was unable to create the formula without the h-g's help. Likewise the h-g was unable to complete as his calculator could not process the longest numbers and he had to rely on my laptop (much against his better judgement!).

I really enjoy the number problems and look forward to them but this one left me a little depressed as I am not sure I could have done it at my skill level. So, my answer your question, Philoctetes, is: Yes it can be done without recourse to the internet - but not unless you have a very good maths grounding.

[Eril]

I also worked it out without using the internet - but I do also have a maths degree, and enjoy recreational maths, so am familiar with the triangular numbers. They do still feature in school maths, however a limited straw poll does indicate that graduates in the liberal arts (inexplicably in my opinion!) don't seem to remember hearing about them. Surely though the hint is in the words used/theme. The obvious first try was to see if the numbers were squares, then I tried out splitting each number into three groups which would form a right triangle. It did take me quite a while before I clicked to the real theme, but even if I didn't know about triangular numbers I could have looked up each possible theme word in the BRB. It is there under 'triangle'. So only (in my opinion) of the same challenge level as say the Mary QoS puzzle, where I had to go to an encyclopaedia (albeit the actual calculations required more effort).

[josuecuginguilua]

Simply add the numbers you want to find the greatest common divisor, and the app will calculate it as you type.

Install it today for Android and iOS and happy calculations!

https://cannatura.org/installGCF.php