HMMT 十一月 2014 · GEN 赛 · 第 7 题
HMMT November 2014 — GEN Round — Problem 7
题目详情
英文原题
- Consider the set of 5-tuples of positive integers at most 5. We say the tuple ( a , a , a , a , a ) is perfect
1 2 3 4 5
if for any distinct indices i , j , k , the three numbers a , a , a do not form an arithmetic progressioni j k
(in any order). Find the number of perfect 5-tuples.
解析
英文解析
- Consider the set of 5-tuples of positive integers at most 5. We say the tuple ( a , a , a , a , a ) is perfect
1 2 3 4 5
if for any distinct indices i , j , k , the three numbers a , a , a do not form an arithmetic progressioni j k
(in any order). Find the number of perfect 5-tuples.
Answer: 780 There are two situations.
( ) ( )
5 3 1