PUMaC 2017 · 团队赛 · 第 11 题
PUMaC 2017 — Team Round — Problem 11
题目详情
- (8) For a sequence of 10 coin flips, each pair of consecutive flips and count the number of “Heads-Heads”, “Heads-Tails”, “Tails-Heads”, and “Tails-Tails” sequences is recorded. These four numbers are then multiplied to get the Tiger number of the sequence of flips. How many such sequences have a Tiger number of 24?
解析
- Note that the number of ”Heads-Tails” and ”Tails-Heads” must be equal or differ by 1. So the possibilities for (number HH, number HT, number TH, number TT) are (2,3,2,2), (2,2,3,2), (3,2,2,2) and (2,2,2,3). The total number of sequences is then 180 . Problem written by Kai Zheng 3 2