Maths Olympiad

Oh, God.

So hard. Most of it.

2 hours. 6 questions.

I could do the first 3, and I'm sure I got them right, and the last 3 were really hard. I still ended up with an answer with all my working written out neatly of how I got the answer, but I'm sure I got the last 3 wrong. I do hope to get some marks for all my working out, though.

I think the first 3 were fairly challenging, but pretty easy in the end.


As an example, here is the first question:

What is the lowest positive integer, made up of only 1's and 0's (in base 10) which is divisible by 12?

If you got 11100 then you are right. At least I hope you are, as that is the answer I got and submitted.

Basically, to get that answer, you have to think about the number in simpler terms.

To be divisible by 12, the number has to be divisible by 3 and 4.

To be divisible by 3, the digits of the number must add up to a multiple of 3.
To be divisible by 4, the last two digits of the number must be divisible by 4.

As the number can only be made up of 1's and 0's, the 1's must add up to a multiple of 3, as adding 0 to anything doesn't change it. Therefore, there must be three 1's as the idea is to find the lowest positive integer.

As the number must be divisible by 4, the last two digits must be divisible by 4. There are already three 1's in the number, and 4 does not divide 01, 10 or 11, so the last two digits must be 0's, as 4 will divide 100.

Thus, the number is 11100.


And that was just question 1. When I first looked at it I though "What??" but half way through another question I figured out how to solve it so I quickly went back to it and wrote it out.

I don't know when I'll find out how well I did, but I'm hoping for a bronze.

I'll probably be disappointed if I don't get anything, but I'd be satisfied with a bronze.

So now we play the waiting game...

RJ