PUMaC 2020 · 组合（B 组） · 第 1 题
PUMaC 2020 — Combinatorics (Division B) — Problem 1
题目详情
- Runey is speaking his made-up language, Runese, that consists only of the “letters” zap , zep , zip , zop , and zup . Words in Runese consist of anywhere between 1 and 5 letters, inclusive. As well, Runey can choose to add emphasis on any letter(s) that he chooses in a given word, hence making it a totally distinct word! What is the maximum number of possible words in Runese?
解析
- Runey is speaking his made-up language, Runese, that consists only of the “letters” zap , zep , zip , zop , and zup . Words in Runese consist of anywhere between 1 and 5 letters, inclusive. Additionally, Runey can choose to add emphasis on any letter(s) that he chooses in a given word, hence making it a totally distinct word! What is the maximum number of possible words in Runese? Proposed by Rishi Dange Answer: 111110 . Solution: At each ”letter” slot, there are 10 options: 5 for the unemphasized letters and 5 1 2 for the emphasized ones. Thus, the maximum total number of words in Runese is 10 + 10 + 3 4 5 10 + 10 + 10 = 111110.