HMMT 十一月 2024 · GEN 赛 · 第 1 题

HMMT November 2024 — GEN Round — Problem 1

Six consecutive positive integers are written on slips of paper. The slips are then handed out to Ethan, Jacob, and Karthik, such that each of them receives two slips. The product of Ethan’s numbers is 20 , and the product of Jacob’s numbers is 24 . Compute the product of Karthik’s numbers.

解析

Six consecutive positive integers are written on slips of paper. The slips are then handed out to Ethan, Jacob, and Karthik, such that each of them receives two slips. The product of Ethan’s numbers is 20, and the product of Jacob’s numbers is 24. Compute the product of Karthik’s numbers. Proposed by: Luke Robitaille Answer: 42 Solution: Each person’s numbers differ by at most 5, so Alice must have 4 and 5. Bob could have 4 and 6 or 3 and 8. Since Alice already has 4, Bob cannot have 4 and 6. So, Bob has 3 and 8. Then the six numbers must be 3 through 8, so Charlie has 6 and 7, multiplying to 42 .