c4countdown

Dinos's puzzle this morning reminds me of another I learned at about the same time. It's probably equally well known, so PM me with an answer, and I'll acknowledge it here if you're right.

Find a 10 digit number in which
the first digit is the number of zeros in the number
the second digit is the number of ones in the number
the third digit is the number of twos in the number
...
the last digit is the number of nines in the number

Liam Tiernan wrote:8100000000?. There are probably others.

How many 8s in that?

Edit: Oh, you deleted it.

Michael Wallace wrote:

Liam Tiernan wrote:8100000000?. There are probably others.

How many 8s in that?

Edit: Oh, you deleted it.

Whoops, soz, serious caffeine deficiency this morning. TBF, was playing weekly poker tournament 'til early hours and won for first time in months. Head still buzzing.

One suggestion by PM so far. Not correct.

Jon Corby spot on at 14:39. Well done.

I've got an extension for this one too, but I need to be careful how I word it. Later, maybe.

Bob de Caux has now got a correct solution.

Jon and Bob have both come up with the same 10-digit number. For you two, and for anyone else who manages a valid solution, how many 10-digit solutions can you find? And can you prove convincingly that there aren't any more?

I might have a stab at a program for this in a bit.

Might.

3rd correct solution. This time from Graeme Cole. Well done, Graeme.

And a correct over-night submission from Dinos.

Kai Laddiman wrote:I might have a stab at a program for this in a bit.

Might.

You'll find it much more satisfying to do it without programming aids.

... unless you simply treat it as an excercise in improving your programming skills. But even then, I'd have a go at doing it by simply thinking.

Ok, first extension.

Replace the asterisks with numbers, which do not have to be single digits, so that the following sentence is correct.

This sentence contains * 0s, * 1s, * 2s, * 3s, * 4s, * 5s, * 6s, * 7s, * 8s and * 9s.

Of course, if any of the asterisks are 1, then you can drop the corresponding plural s.

I believe there are two solutions.

Another correct submission for the 10 digit number. This time from Ben W.

For the first extension, Bob is the first to get one of the two possible answers.

So who's going to be the first to get them both?

Howard Somerset wrote:So who's going to be the first to get them both?

Is this another extension? If it is, I'm going for Bob.

Jon O'Neill wrote:

Howard Somerset wrote:So who's going to be the first to get them both?

Is this another extension? If it is, I'm going for Bob.

I wonder if Bob will hold back, just to prove you wrong, Jono.

First the first extension, Jon Corby's the first to get both solutions.

So I failed the second extension? Poop.

Jon O'Neill wrote:So I failed the second extension? Poop.

Sorry Jono, I couldn't handle the pressure and went to pieces

Bob has now recovered his composure, and come up with the second possible solution.

And now a correct submission from Jono. Well half a submission anyway. One solution to the extension.

All correct now from Jono. Both for the initial puzzle, and the two solutions for the extension.

10 digit solution now correctly found by Jack.