Apr. 23rd, 2011 12:40 pm
lederhosen: (Default)
[personal profile] lederhosen
Working through boxes. Today I got to some of my old Maths Olympiad material. I feel sad to throw that stuff out - it was one of the biggest things in my school life - but there's way too much to keep it all.

One of my favourite competitions was Tournament of the Towns, which was run from Russia. We'd sit down, attempt the problems, and then our efforts would be sent off to Russia by sea-mail. Then they'd be marked, and sent back (again by sea-mail) so it would be about six months before we found out our results. (Looking at my old papers, I feel sorry for the poor markers who had to read my utterly awful handwriting. One of the best things I ever did was give up on cursive. And English wouldn't even have been their first language.)

It had a couple of nifty features: if you did well you got a diploma in Cyrillic (I have a few somewhere around), and the problems had a different flavour to the ones I got in most Australian/US competitions. The Russian ones tended to be quite simple to state, but no easier to solve.

The marking scheme was pretty simple: IIRC it went 0 for no attempt, - for efforts towards a solution, ± for a mostly complete solution, and + for a complete solution. But occasionally they'd give out a +! for a solution they really liked (i.e. better than theirs). This was one of the things I liked about TotT; most contests, a proof was a proof and if it had no holes you got full marks. But for me, an elegant proof that cuts to the heart of the matter is worlds away from a plodding grindy one, and occasionally I managed to get that prized +!.

Anyway, here's one I found today, from the November 1990 junior paper:

An 8 by 8 square is painted white. We are allowed to choose any rectangle consisting of 3 of the 64 (1 by 1) squares and paint each of the 3 squares in the opposite colour (the white ones black, the black ones white). Is it possible to paint the entire square black by means of such operations?

Anybody want to try it? I'll post up my solution in a couple of days.


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