HMMT 二月 2002 · ADV 赛 · 第 2 题
HMMT February 2002 — ADV Round — Problem 2
题目详情
英文原题
- A certain cafeteria serves ham and cheese sandwiches, ham and tomato sandwiches, andtomato and cheese sandwiches. It is common for one meal to include multiple types ofsandwiches. On a certain day, it was found that 80 customers had meals which containedboth ham and cheese; 90 had meals containing both ham and tomatoes; 100 had mealscontaining both tomatoes and cheese. 20 customers’ meals included all three ingredients.
How many customers were there?
解析
英文解析
- A certain cafeteria serves ham and cheese sandwiches, ham and tomato sandwiches,
and tomato and cheese sandwiches. It is common for one meal to include multiple types ofsandwiches. On a certain day, it was found that 80 customers had meals which containedboth ham and cheese; 90 had meals containing both ham and tomatoes; 100 had mealscontaining both tomatoes and cheese. 20 customers’ meals included all three ingredients.
How many customers were there?
Solution: 230 . Everyone who ate just one sandwich is included in exactly one of the first three counts, while everyone who ate more than one sandwich is included in all fourcounts. Thus, to count each customer exactly once, we must add the first three figures andsubtract the fourth twice: 80 + 90 + 100 − 2 · 20 = 230.