James’ 10-digit number challenge

First of all, watch the video of James’ challenge. It’s only a minute long:


If you want to have a go at working it out yourself, STOP READING NOW, SPOILERS AHEAD!

Right then, I thought I’d see how far I could get with logic, since I’m no mathematician. So I wrote down
_ _ _ _ _ _ _ _ _ _

And immediately realised the first digit could not be 0, as that would be self contradictory. And thinking about 9s, I thought there couldn’t be any of those, because if the Zeros can’t be 0, then they have to be 9, which means the Nines would have to be 1, which means there aren’t 9 Zeros any more.

How about 8 Zeros? That means we have to put at least a 1 in the Eights… Which means there must be a non-zero Ones, which only leaves 7 Zeros left, which is a contradiction.

Similarly, 7 Zeros doesn’t work out by similar logic.

6 Zeros? Okay, that means non-zero Sixes, so let’s try a 1 there:
…which means the second digit must be non-zero, and non-one too, since that would be two Ones. How about 2?….
Oh, hang on, that means we’ve got a Two. But only one of them…
So, what about the rest of those Xs?
Oh, hang on…. There are 6 of them! So that’s…

Which has 6 Zeros, 2 Ones, 1 Two, and 1 Six. It works!

Thanks for the fun challenge, James!


James on Twitter: https://twitter.com/jamesgrime

Me on Twitter: https://twitter.com/TheVoidTLMB