Question 1
Let $n\ge2$. Carl has $n$ books, with distinct heights and distinct widths, initially arranged from left to right in increasing height. A move swaps two adjacent books when the left book is wider and shorter than the right book. He continues until no move is possible. Prove that every sequence terminates and the final order is increasing in width.
Proposed by Milan Haiman. Evan Chen’s third-party compilation; source discussion https://aops.com/community/p15952780. Source video https://youtu.be/r7j0oRtpErA?t=1190.
Proposed by Milan Haiman. Evan Chen’s third-party compilation; source discussion https://aops.com/community/p15952780. Source video https://youtu.be/r7j0oRtpErA?t=1190.