# Bmo 2023/24

how did everyone find it

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thought it was a bit harder than previous years - might just be me tho. Geometry was quite tough I thought.
Original post by EesaImran
thought it was a bit harder than previous years - might just be me tho. Geometry was quite tough I thought.

yes id agree i feel like the first question needing a full proof to go with the answer made it take so much longer
Original post by libgensym
yes id agree i feel like the first question needing a full proof to go with the answer made it take so much longer

My classmates and I found the questions are easier this year. We both are year 9 students.

I did all 6, my friend completed 4.
(edited 3 weeks ago)
Original post by libgensym
how did everyone find it

My friend and I found the questions are easier. We are year 9 students
Original post by Juni2704
My classmates and I found the questions are easier this year. We both are year 9 students

yh i think it varies from person to person, i struggle with geometry and combinatoric sort of questions so found this year harder
Original post by Juni2704
My friend and I found the questions are easier. We are year 9 students

how many questions did u attempt?
Original post by EesaImran
how many questions did u attempt?

I did all 6, my friend completed 4.
Original post by libgensym
how did everyone find it

My son year 10 found it harder this year . He got a distinction last year (29 from 3 questions answered) . His qualification score this year was 117. I think it all depends on where your strengths lie some will find harder some easier but difficult to judge until the scores are out.
This is the first time doing BMO1 (year 11). I found it to be slightly more difficult than previous past papers. I answered half of Q1, fully answered Q2,Q4 and Q5.
What do you reckon the grade boundaries for distinction will be?
Question: For Q4, if half of my proof was based on an assertation that was wrong, but I end up obtaining one of the 2 possible values for n, how many marks would I lose?
Another question: How would the markers mark Q5, the answer is quite easy to obtain (250) but how rigorous does your proof need to be?
Another question: For Q2, is it enough to show that if 2 numbers in the sequence differed by k, then the next number will never be consecutive unless k is 1?
Another question: For Q1, if I didn't get an answer, but I noticed the fact that if you shift one of the letters to the left, all the letters that have been passed by that letter can't move (e.g. OLYMSPIAD, S is shifted to the left so PIAD cannot move), how many marks would I get for that?

Sorry for dumping these questions on you guys, but as I said, this is the first BMO I have ever done. I did do the hamilton last year, but I'm not sure if they mark it in the same way. I would also appreciate it if someone explained to me how BMO1 is marked.
(edited 3 weeks ago)
Original post by kmannnn
Question: For Q4, if half of my proof was based on an assertation that was wrong, but I end up obtaining one of the 2 possible values for n, how many marks would I lose?
Another question: How would the markers mark Q5, the answer is quite easy to obtain (250) but how rigorous does your proof need to be?
Another question: For Q2, is it enough to show that if 2 numbers in the sequence differed by k, then the next number will never be consecutive unless k is 1?
Another question: For Q1, if I didn't get an answer, but I noticed the fact that if you shift one of the letters to the left, all the letters that have been passed by that letter can't move (e.g. OLYMSPIAD, S is shifted to the left so PIAD cannot move), how many marks would I get for that?

Sorry for dumping these questions on you guys, but as I said, this is the first BMO I have ever done. I did do the hamilton last year, but I'm not sure if they mark it in the same way. I would also appreciate it if someone explained to me how BMO1 is marked.

For marking - They use a 0+ 10- mark-scheme, This is the 2022 (round 1) report's description of how they mark:

"What we are looking for are full solutions to problems. This involves identifying a suitable strategy, explaining why your strategy solves the problem, and then carrying it out to produce an answer or prove the required result. In marking each question, we look at the solution synoptically and decide whether the candidate has a viable overall strategy or not. An answer which is essentially a solution will be awarded near maximum credit, with marks deducted for errors of calculation, flaws in logic, omission of cases or technical faults. On the other hand, an answer which does not present a complete argument is marked on a ‘0 plus’ basis; up to 4 marks might be awarded for particular cases or insights."

So I'd guess you will have got 2-4 marks for q1.

For question 5, to get full or near full marks you'll need to prove 250 flaws can be achieved, and that it is the smallest amount obtainable.

I dunno about your answer to question 2, I used strong induction for my proof. They look at differences in the video solutions, so you've got that going for you.
Original post by dan3214
For marking - They use a 0+ 10- mark-scheme, This is the 2022 (round 1) report's description of how they mark:

"What we are looking for are full solutions to problems. This involves identifying a suitable strategy, explaining why your strategy solves the problem, and then carrying it out to produce an answer or prove the required result. In marking each question, we look at the solution synoptically and decide whether the candidate has a viable overall strategy or not. An answer which is essentially a solution will be awarded near maximum credit, with marks deducted for errors of calculation, flaws in logic, omission of cases or technical faults. On the other hand, an answer which does not present a complete argument is marked on a ‘0 plus’ basis; up to 4 marks might be awarded for particular cases or insights."

So I'd guess you will have got 2-4 marks for q1.

For question 5, to get full or near full marks you'll need to prove 250 flaws can be achieved, and that it is the smallest amount obtainable.

I dunno about your answer to question 2, I used strong induction for my proof. They look at differences in the video solutions, so you've got that going for you.

Could you answer my question about Q4 and half of my proof being wrong? Would I receive a 0+ mark or a 10- mark?
Original post by kmannnn

Could you answer my question about Q4 and half of my proof being wrong? Would I receive a 0+ mark or a 10- mark?

I think it depends on how rigorous and well-reasoned the rest of your answer is. Also the reason why you didn't get both answers for n will mean alot I imagine, if you didnt get them because your method and reasoning was ultimately flawed then it'll be a 0+, but if you had a solid method which should have worked if not for maybe a wrong assumption or mistake or two then I imagine it'll be 10-. Just my thoughts though its my first bmo too. I really hope the boundaries are quite generous this year.
Original post by dan3214
I think it depends on how rigorous and well-reasoned the rest of your answer is. Also the reason why you didn't get both answers for n will mean alot I imagine, if you didnt get them because your method and reasoning was ultimately flawed then it'll be a 0+, but if you had a solid method which should have worked if not for maybe a wrong assumption or mistake or two then I imagine it'll be 10-. Just my thoughts though its my first bmo too. I really hope the boundaries are quite generous this year.

Yeah,

What I did was notice that n2^n + 1 has to be an odd square, not an even square, so n2^n + 1 = (2k+1)^2
Minus 1 from both sides, then completing the square yields the equation: n2^n = 2k(2k+2)
Divide by 4: n2^(n-2) = k^2 + k
Rearrange to get k^2 + k - n2^(n-2) = 0
What I should have done is notice that n2^(n-2) can only be 2 or 6 for k to be an integer, so n can be 2 or 3. This is because the quadratic is only factorizable if n2^(n-2) is 2 or 6.
Instead what I did was complete the square and find k in terms of n, from which I was able to find 1 possible value for n (3).
Original post by dan3214
I think it depends on how rigorous and well-reasoned the rest of your answer is. Also the reason why you didn't get both answers for n will mean alot I imagine, if you didnt get them because your method and reasoning was ultimately flawed then it'll be a 0+, but if you had a solid method which should have worked if not for maybe a wrong assumption or mistake or two then I imagine it'll be 10-. Just my thoughts though its my first bmo too. I really hope the boundaries are quite generous this year.

Yeah same, I hope the grade boundary for distinction is a bit lower than usual (high 10s/low 20s).
I've heard from some acquaintances that they felt questions this year seem much easier. It appears that the grade boundaries may be quite high this year.
(edited 2 weeks ago)
Original post by Juni2704
I've heard from some acquaintances that they felt questions this year seem much easier. It appears that the grade boundaries may be quite high this year.

I think you can argue both ways. Question 1, supposedly being the most accessible, needed an actual proof which makes it harder, however Q2 and Q5 were surprisingly easy. Also, in my opinion, last year's paper was easier so the grade boundaries might go down.
(edited 2 weeks ago)
Original post by kmannnn
I think you can argue both ways. Question 1, supposedly being the most accessible, needed an actual proof which makes it harder, however Q2 and Q5 were surprisingly easy. Also, in my opinion, last year's paper was easier so the grade boundaries might go down.

Interesting analysis. A considerable number of school students did not perform well in SMC this year, and only a few progressed to the BMO1 round. There was an anticipation that the BMO1 boundary would be lower than the previous year, but it turned out not to be the case. So, let’s see what will happen to the BMO1 results.

I’ve heard that kids from specific countries directly enter the BMO1 without taking the SMC. This could potentially screw up the BMO1 results.
(edited 2 weeks ago)
Hungary camp invitation sent out last Thursday.

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