Bushy and Jumpy return with 2021 walnuts!
Source: IMOC 2021 C3
August 11, 2021
combinatorics
Problem Statement
Two squirrels, Bushy and Jumpy, have collected walnuts for the winter. Jumpy numbers the walnuts from 1 through , and digs little holes in a circular pattern in the ground around their favourite tree. The next morning Jumpy notices that Bushy had placed one walnut into each hole, but had paid no attention to the numbering. Unhappy, Jumpy decides to reorder the walnuts, and Bushy decides to interfere with Jumpy. The two take turns to reorder the walnuts. Each time, Bushy chooses walnuts and reorders them and then Jumpy chooses walnuts to reorder. Find the least positive integer such that whatever Bushy does, Jumpy can ensure that the th hole from the left has the th walnutIft0501