Thursday, January 15, 2009

Quickie

I got a Math-Problem-a-Day Calendar for Christmas. It's kind of a disappointment because the answer to each problem is the number of that day and a lot of these are barely even math problems, such as 20+0*sqrt(9).

That said, it is definitely possible to have good math problems where you know the final answer but the puzzle is how to get there. Yesterday's, which I just finally solved today, is a good example.

2.8 + 2.24 + 1.792 + 1.4336 + 1.14688 + 0.917504 + ...

The sum is yesterday's date, 14. But I couldn't figure out what this series was until someone (who happens to have this same calendar, btw) stopped by my office and mentioned Ramanujan. That got us talking about continued fractions (i.e. "I don't get continued fractions." "Me neither."). Which is all the hint I'm going to give for now...

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