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Hi, I keep on thinking I've solved this, but always fall down with 15a. Is it a type g ending in 76 please?

Hi, gitto,

Yes, 15 has property g: it is a triangular number. An earlier post explained that, of the eight possible triangular numbers (1, 3, 6, 10, 15, 21, 28, 36), 6 and 28 are perfect numbers, 1 is a fourth power, and 36 is a square, so leaving just enough answers for the required four triangular numbers.

15 does indeed end in 76, and there’s only one four-digit triangular number that fits.

Thanks wintonian, I’ll try again, but I don’t see how that single answer fits with the s multiplier that keeps coming out as 353 - I’ll persevere by ignoring the s’s as long as possible!

Hi, gitto,

The three clues with property s (number whose reverse is divisible by the number) are 11, 22 and 33. The answer to 33 is indeed 353, and there are only two four-digit numbers that are not palindromes (because this implies a multiple of 1, and this has been used up by 33) but whose reverse is divisible by the number. One of these, the answer to 11, fits with the only possible answer for 15.

I found the two numbers by searching on the internet, but I don’t think it takes too long to work them out manually.

I think this works for the 4-digit reversal with a multiplier of 9;

1000d + 100c + 10b + a = 9000a + 900b + 90c + 9d

991d + 10c = 8999a + 890b

Because they both have 4 digits, a must be 1 and d must be 9, so

10c = 80 + 890b

c = 8 + 89b

therefore b = 0

Similarly for the 4-digit reversal with a multiplier of 4;

1000d + 100c + 10b + a = 4000a + 400b + 40c + 4d
996d + 60c = 3999a + 390b

Because they both have 4 digits, a must be 2 and d must be 8, so

7968 + 60c = 7998 + 390b
60c = 30 +390b
2c = 1 + 13b
b = 1

... those should read Because they are reversals

Oyler : Yes, I don't dispute that the number puzzles have been around a long time. I said "...at some point...", which encompasses that.

What I do dispute, on a forum frequented by many people who have no contact with the 'Listener clique', is use of an acronym such as SSS, shared by only a few people. In fact, you yourself seem to sense this, since you also spell out what you think SSS stands for.

Actually, a good deal more people (I mean tens or hundreds of thousands of people) know SSS to be 'Skin So Soft', which is a cosmetic favoured for its midge-repellent properties. I can vouch for its usefulness. If you want to award yourselves a tube of midge repellent, I'd heartily endorse this as a step in the right direction...the TTT (Tatty Tin Tray) does smack of self-importance, and at least people would see that there is an element of making fun of yourselves if you award a tube of midge-repellent instead...

In response to smellyharry's enquiry about alternatives to spreadsheets, those who are at all familiar with computer programming might like to try using python. This is a computer language which you can install on a computer and has an interpreter interface, which means you can enter a command and get an immediate response back, rather than having to write a program, then compile and run it.
For number puzzle enthusiasts like me it has a very useful feature called List Comprehensions, so you can type for example [n*(n+1)/2 for n in range(1,1000)] and get output a list of the first 1000 triangular numbers. Nowadays I would use python in preference to a spreadsheet.

For those interested in learning python, there's usually a MOOC available somewhere or other.