ukmt Hamilton olympiad

Hi there, I have my ukmt Hamilton olympiad next Thursday and I would really appreciate if anyone could reply with tips and tricks as well as topics that come up frequently on the olympiad (what often comes up for algebra, logic questions and geometry)! thanks

Does anyone know how harsh the markers are for the hamilton?

For q4, if I simply wrote down some facts that I could derive from the information given, as I didn't know how to do the question. Could I potentially get 1 or 2 marks from that?


edit:
I also have another question, when does the paper come out, and when do the results themselves also come out?

Does anyone know how harsh the markers are for the hamilton?

For q4, if I simply wrote down some facts that I could derive from the information given, as I didn't know how to do the question. Could I potentially get 1 or 2 marks from that?


edit:
I also have another question, when does the paper come out, and when do the results themselves also come out?

Speaking from experience, if you think you kind of solved the problem you'll get 3/10 and if you think you'll get a couple of marks for observations you'll probably get 0/10 unfortunately. The observations have to be really quite crucial to the argument to get 1 (maybe 2) marks. I haven't seen the paper though (but I've heard that there was 3 diophantine equations...)

What is the criteria to get 10/10?

If you forgot a combination what would you get on the question? I've heard that you get around a 7/10, but that seems a bit harsh for forgetting 1 combination.

Also what would you expect the grade boundaries to be for bronze medal/distinction?

(Sorry for bombarding you with questions! I just had to ask.)

To get 10/10 you need to produce a logical argument with proofs / justifications of every assertion. Lack of proof / justification limits you to 3/10. If you have a problem with like 3 cases and you miss a case you'll probably get 7/10 but if there's 3-5+ cases which come after some previous observations you'll probably get 9 (maybe 8). Arithmetical errors with little effect on the rest will also give 9/10. The marking is very harsh so its better to keep expectations relatively low (and possibly get pleasantly surpised) rather than thinking they'll give marks and then getting annoyed when you get lower than you expected.

As for expected boundaries, I haven't seen the paper (I did the Maclaurin Olympiad) but they'll probably be higher than last year since last year's paper was really hard. Generally its like 48-52 for Gold (top 20), 42-26 for Silver (top 50) and 36-40 for Bronze (top 100)

Did anyone else answer Q5? I answered it but it don’t know how well I explained it. What did you get?

I did.

I got 4047 and any multiple of 4.

If you have 4047 consecutive integers with 2023 being the smallest, and you continously take the 2 largest integers and replace them with their difference, at some point you end up with 1 2023 and 2023 1s. You can now see that if you continue taking the 2 largest integers and finding their difference, you end up with 0.

Any multiple of 4 also works, because if you continously take the 2 largest integers and find their difference, you end up with an even number of 1s. From this you can see that if you continue taking the 2 largest integers and replace them with their difference, you end up with 0.

(This is a kinda rough explanation. I phrased it better in the actual during the actual challenge.)

Yh I got the same!
For q3 did anyone else get 757,576?
(I got this by realizing that 1/any number greater than 5 to 10 has a first non zero digit of one.
I then counted 26 to 100, 2501 to 10,000, 250,001 to 1,000,000 and of course 1

Yh I got the same!
For q3 did anyone else get 757,576?
(I got this by realizing that 1/any number greater than 5 to 10 has a first non zero digit of one.
I then counted 26 to 100, 2501 to 10,000, 250,001 to 1,000,000 and of course 1

I got the same, but I also said that if it’s 4047 plus a multiple of 4, that would work too (It would be 0 as it’s 4047 and then the even number of ones after that). I’m not sure if that’s right or not, though.

Which questions did you get?
(I got 1,2,3,5 and 11^2+ 3600 =61^2 (in hope of a free mark on q6)