Y by Functional_equation, centslordm, InternetPerson10, Mathmick51, TheStrayCat, megarnie, Aritra12, 554183, adityaguharoy, Aopamy, yshk, deplasmanyollari, eggymath, Kingsbane2139, Rounak_iitr, Funcshun840, cubres
Two squirrels, Bushy and Jumpy, have collected 2021 walnuts for the winter. Jumpy numbers the walnuts from 1 through 2021, and digs 2021 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 by performing a sequence of 2021 moves. In the
-th move, Jumpy swaps the positions of the two walnuts adjacent to walnut
.
Prove that there exists a value of
such that, on the
-th move, Jumpy swaps some walnuts
and
such that
.


Prove that there exists a value of





This post has been edited 2 times. Last edited by popcorn1, Jul 20, 2021, 8:40 PM