29

Part of 2017 Harvard-MIT Mathematics Tournament

Problems(1)

2017 Guts #29: Cycle factoring

Source:

Yang has the sequence of integers

1, 2, \dots, 2017

2016

swaps in order, where a swap changes the positions of two integers in the sequence. His goal is to end with

2, 3, \dots, 2017, 1

. How many different sequences of swaps can Yang do to achieve his goal?