Over four months in now, and I've decided to make my first substitution; it dawned on me that I hadn't been using a monthly face mask since the first month (although you will be glad to hear that I use a moisturising face scrub at least every other day), and it didn't feel quite right that this was going to be something that I couldn't make up.

So I've substituted "Solve twenty-five of the problems on Project Euler" for number 82, which was previously the monthly face mask. Project Euler is a site that posts challenging maths and computing puzzles, and there are over two hundred of them now. I think this is a challenge that will really appeal, as some of the puzzles do have "brute force" solutions - such as number 6, the one that I am considering first - i.e., you could solve it with a program that would obtain the answer through simply performing the required operations, but there is always the probability that there is a more elegant solution. With a bit of careful thought one should be able to find the answer...

I'm going to try and solve the first ten problems, and then see which other fifteen take my fancy.

More soon on other things!

## Friday, 29 August 2008

### Substitution

Posted by
NathanRyder
at
2:18 pm

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## 1 comment:

What? That problem is really quite simple...

Both of the sums in question have closed forms that are easily proven via induction, so the difference is very easy to compute for any n.

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