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Anyone else take it?

How did you think it was? I thought it was quite hard, a lot harder than last year's imho. I managed to completely do 1 and 2, and did q4 but my reasoning might not have been completely correct (I got 504 for q4).

Hope everyone did well...

How did you think it was? I thought it was quite hard, a lot harder than last year's imho. I managed to completely do 1 and 2, and did q4 but my reasoning might not have been completely correct (I got 504 for q4).

Hope everyone did well...

Scroll to see replies

theone

Anyone else take it?

How did you think it was? I thought it was quite hard, a lot harder than last year's imho. I managed to completely do 1 and 2, and did q4 but my reasoning might not have been completely correct (I got 504 for q4).

Hope everyone did well...

How did you think it was? I thought it was quite hard, a lot harder than last year's imho. I managed to completely do 1 and 2, and did q4 but my reasoning might not have been completely correct (I got 504 for q4).

Hope everyone did well...

can you remember any of the questions?

Ralfskini

can you remember any of the questions?

1. Solve the simultaneous equations:

ab + c + d = 3

bc + d + a = 5

cd + a + b = 2

ad + b + c = 6.

2. ABCD is a rectangle, P is the midpoint of AB, and Q is the point on PD such that CQ is perpendicular to PD.

Prove that the triangle BQC is isosceles.

3. Alice and Barbara play a game with a pack of 2n cards, on each of which is written a positive integer. The pack is shuffled and the cards laid out in a row, with the numbers facing upwards. Alice starts, and the girls take turns to remove one card from either end of the row, until Barbara picks up the final card. Each girl's score is the sum of the numbers on her chosen cards at the end of the game.

Prove that Alice can always obtain a score at least as great as Barbara's.

4. A set of positive integers is defined to be wicked if it contains no three conesecutive integers. We count the empty set, which contains no elements at all, as a wicked set.

Find the number of wicket subsets of the set {1,2,3,4,5,6,7,8,9,10}.

5. Let p, q and r be prime numbers. It is given that p divides qr-1, q divides pr-1 and r divides pq-1. Find all possible values of pqr.

2776

Did it, did q1, (got about half of it) then did the triangle geometry ques. (think I nailed that one)

BTW, how did u prove q1?

BTW, how did u prove q1?

It's a long laborious process of subtracting and factorising certain equations in order to derive 2b+d = 3 and a+c = 2. then the result follows from substitution into the first equation.

theone

It's a long laborious process of subtracting and factorising certain equations in order to derive 2b+d = 3 and a+c = 2. then the result follows from substitution into the first equation.

I subtracted etc and got like (c-1)(x-x)=3 etc etc

and did it for every single one. Then I took c-1=3, -3, -1, 1

And got 2003 for the answer

2776

Yes, i assumed that it is an interger and that the other side gives 1, and I know thats not really rigerous proofs, but that direction looked so inviting and looked like a pattern, no?

Quoting the instructions on the handout we got:

'Full proofs are expected not conjectures based on pattern spotting'.

i did the same as you and i got the answer for question 4 is 504, that's definitely the right answer for q4. This is my first time, and I'm not a british, i'm a vietnamese student who is doing first year A-level in London. I wonder that when will the result come out and how can we know the qualifying mark for the next round. Thanks a lot !

- Advice for Maths Olympiads
- Is it too late for serious progress at BMO1/BMO2
- Bmo 2023/24
- is olympiads important?
- BMO1/BMO2 Preparation
- How to get better at BMO1
- Smc & bmo
- Senior Maths Challenge 2023
- BMO Prep
- BMO1 help
- SMC-BMO
- Year 12 | a realistic GYG
- Should I bother putting Cayley/Hamilton/Maclaurin Olympiad medals in Maths PS
- School won’t enter student for UKMT maths challenge
- Geometry in bmo & smc
- How valuable are maths olympiads when applying for physics?
- SMC Prep
- How exactly are marks awarded in BMO??
- UKMT prep?
- Solving Diophantine equations in math competitions

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