by Gilbert Keith
So, yaah. I took the aime last Tuesday Dag, the thing was so ghetto. I did problems 1,3 and 4 in 15 minutes. That elevated my spirits a lot. I got stuck on problem 4, however for 30 minutes until I looked for what for they wanted the numbers in. See, I just realised that it helps a lot to read the question in its entireity rather than just thinking about how to tackle it first. Then, I started working on other problems, until I realised that my efforts were futile. I tried 14 for a while, which dealt with triangular pyramids and stuff. Basically, I think I got somewhere with my solution; but, when I verified my work with Richard, it seemed radically different. Well, I just guessed 12 on that one.
There were a couple of questions on there that I could have brute forced. #6 for example, would have been easy:
Let be the set of real numbers that can be represented as repeating decimals of the form where are distinct digits. Find the sum of the elements of .
I just didn’t want to brute force it and was thinking of elegant ways to solveit. #11 was also pretty easy:
A collection of 8 cubes consists of one cube with edge-length for each integer A tower is to be built using all 8 cubes according to the rules:
Any cube may be the bottom cube in the tower.
The cube immediately on top of a cube with edge-length must have edge-length at most
Let be the number of different towers than can be constructed. What is the remainder when is divided by 1000?
#12, the trig problem was pretty good. I only realised the trick when I was volunteering for NHS .
So, Lessons learnt:
- First 5 are pretty easy (and, counting is pretty easy to learn)
- 2-3 problems are brute-forcable, and they should be attempted prior to attempting the impossible.
- Du intense practise the weekend before the aime.
- Last, but not the least, Amy didn’t du the Aime! :p