AIM Tech math quiz will take place on August 24, at 15:00 MSK. Quiz prepared for Petrozavodsk Summer Camp participants, but everybody is welcome to join. You could participate in teams of one or two persons. All problems could be solved by pen, paper and calculator, but you could use computer as well. Using internet for solving problems is forbidden. Quiz duration is 2h.

In order to participate you should register on the website and fill the form: Registration link. Form should be filled before start of the quiz, Thanks to bobrdobr for the platform! It is rather new and available only in Russian, but all problems will have English statement as well.

Link to quiz itself (will be active when contest starts).

**UPD.**

Link to the problems with answers. Click "Показать решение" to see the answer.

Final scoreboard. Congratulations to the winners!

Should we use one account for both team members?

Yes

Will there be an official editorial? Else, could anyone share solution of Q21, 25, 28? For 25 I brute forced small values upto #cars = 15, but I couldn't find any patterns.

will there be a leaderboard to check the results ?

:))))

I also figured out there is a scoreboard after contest!!!

link is after problem 30.

Didn't notice , thanks.

can we upsolve problems?

On problem 19: we used to think, by mistake, that the answer is 28 (the strategy is like with the two ordinary eggs, but we try them two at a time), and now we think that the answer is 24 (because we wrote a dp). We decided to accept both answers (because there is an interpretation of the statement where 28 is correct)

In our dp[N] we have 3 cases:

we break an egg at floor Z than we must throw another two eggs at floors 1, 2, .., Z — 1 -> it spend 1 + (2*Z — 2) turns

we throw a second egg at floor Z and it breaks, then we know that the third egg is real and we can throw only this egg on the floors 1, 2, .., Z — 1 -> it spend 2 + (Z — 1) turns

we have three eggs and know that Answer > Z and now we can throw eggs only in [Z + 1, N], it is the same as dp[N — Z].

That dp answers 27. Can someone help to find a bug in the idea?

Why is such strategy necessarily optimal? I mean, trying second egg on the same floor if the first one survived and so on

first one can be rubber egg, and we don't know if the egg breaks from that floor

And why should we get this information by immediately trying a second egg on the very same floor?

I think that is the bug. Thanks.

If one is interested, one of us has devised the strategy on paper, and it looks like throwing eggs in turn on floors where each time we lift up fewer and fewer floors until one egg breaks, then do something straightforward

Here is the upsolving: https://mathmaker.ru/contests/12eaac24-15d2-4d19-9afb-6e303ecba55e

Here you can find the answers: https://mathmaker.ru/q/a0217810-2da4-4efd-b118-bf0a8587a743/

Open any problem you want, there will be a button "show the answer" or something