PUMaC 2021 · 团队赛 · 第 1 题
PUMaC 2021 — Team Round — Problem 1
题目详情
- An evil witch is making a potion to poison the people of PUMAClandia. In order for the potion to work, the number of poison dart frogs cannot exceed 5, the number of wolves’ teeth must be an even number, and the number of dragon scales has to be a multiple of 6. She can also put in any number of tiger nails. Given that the stew has exactly 2021 ingredients, in how many ways can she add ingredients for her potion to work? gcd( x,y )gcd( y,z )
解析
- An evil witch is making a potion to poison the people of PUMAClandia. In order for the potion to work, the number of poison dart frogs cannot exceed 5, the number of wolves’ teeth must be an even number, and the number of dragon scales has to be a multiple of 6. She can also put in any number of tiger nails. Given that the stew has exactly 2021 ingredients, in how many ways can she add ingredients for her potion to work? Proposed by: Nancy Xu Answer: 1011 It is equivalent to find the sum of the number of nonnegative multiples of 6 less than 2016, 2018, and 2020, which is 377 × 3 = 1011. gcd( x,y )gcd( y,z )