HMMT 十一月 2025 · THM 赛 · 第 1 题

HMMT November 2025 — THM Round — Problem 1

Mark has two one-liter flasks: flask A and flask B . Initially, flask A is fully filled with liquid mercury, and flask B is partially filled with liquid gallium. Mark pours the contents of flask A into flask B until flask B is full. Then, he mixes the contents of flask B and pours it back into flask A until flask A is full again. Given that the mixture in flask B is now 30% mercury, and the mixture in flask A is x % mercury, compute x .

解析

Mark has two one-liter flasks: flask A and flask B . Initially, flask A is fully filled with liquid mercury, and flask B is partially filled with liquid gallium. Mark pours the contents of flask A into flask B until flask B is full. Then, he mixes the contents of flask B and pours it back into flask A until flask A is full again. Given that the mixture in flask B is now 30% mercury, and the mixture in flask A is x % mercury, compute x . Proposed by: Derek Liu Answer: 79 Solution: Since flask B is now 30% mercury, it must also have been 30% mercury (and hence 70% gallium) when it was full. For this to occur, Mark must have initially poured 0 . 3 liters of mercury from flask A into flask B . Thus, Mark also poured 0 . 3 liters of mixture from flask B into flask A , so flask A ended up with 0 . 3 · (70%) = 0 . 21 liters of gallium. The remaining 79 % is mercury. Remark. Answers 79% and 0 . 79 instead of 79 were also accepted.