MathDB

C3

Part of 2021-IMOC

Problems(1)

Bushy and Jumpy return with 2021 walnuts!

Source: IMOC 2021 C3

8/11/2021
Two squirrels, Bushy and Jumpy, have collected 20212021 walnuts for the winter. Jumpy numbers the walnuts from 1 through 20212021, and digs 20212021 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 12321232 walnuts and reorders them and then Jumpy chooses nn walnuts to reorder. Find the least positive integer nn such that whatever Bushy does, Jumpy can ensure that the iith hole from the left has the iith walnut
Ift0501
combinatorics