Bmo 2024

How did everyone do? I did five questions (1-5) but sillied geometry, so thats about 4 questions right. Any predictions for merit, distinction, and medal awards this year?

I think it was an easy paper, Q6 I found way too easy; it was just pigeonhole principle I think...
Q4 (Geometry) was horrible though

How did you solve Q6 using just the pigeonhole principle?

I think it was an easy paper, Q6 I found way too easy; it was just pigeonhole principle I think...
Q4 (Geometry) was horrible though

I'm surprised a lot of people are finding Q4 difficult, personally I didn't have too much issues. I didn't get Q6 though like you, tbh I didn't even spend any time on it bc i just assumed my time would be better spent working on Q5 (for which I got an (almost) full solution I think)

Not worked it through/seen the solution, but Id imagine you could consider how many are one unit away (squared distance, so share a face) two units away (share an edge) three units away (share a vertex) etc up to 27 units away (max squared distance), and argue pigeonhole from those numbers. Though you might have to be careful about assuming unit cubes are different colours in the arguments for different distances.
Id guess working it with a 4*4 2d grid (or even smaller) might give the basic insight.

I can’t see how that would work

16 possible distances.
Pigeonhole shows there must be at least 22 of one type.
22 = 16a+b
B = 6.
Pigeonhole shows there must be 6 pairs

I agree that there are at least 22 cubes of one type, where does 16 come from? And where does 22 = 16a + b come from?