^{29}, expressed in base 10, is a nine-digit number. All nine of its digits are different. Find the digit that is missing without explicitly calculating 2

^{29}. (Thanks to Kate for this one; a solution is there, so don't look until you've thought about it.)

## 7 comments:

I like it!

Oh, this is so uninteresting! The puzzle is too amenable to a calculator-based solution.

Got it. Very nice.

Got it (I think) and I'd have to suggest to Vishal at number 2 that the non-calculator trick is quite cute.

Yemon

Cool. I got it. It's one of those problems that's a lot easier if you trust Kate and assume a solution exists.

Problems like this crop up at local math competitions from time to time (at least they did in my area). It's the kind of problem that ensnares people too used to their calculators, which is why I like it.

I read the solution at Kate's page.

The solution is not easy and not fast at all. It's a problem to solve with a calculator, too many time spent.

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