MathDB
2021 Combo Div 2 P1

Source:

March 2, 2021
combinatorics

Problem Statement

We have a 99 by 99 chessboard with 99 kings (which can move to any of 88 adjacent squares) in the bottom row. What is the minimum number of moves, if two pieces cannot occupy the same square at the same time, to move all the kings into an XX shape (a 5×55\times5 region where there are 55 kings along each diagonal of the XX, as shown below)?
\begin{tabular}{ c c c c c } O & & & & O \\ & O & & O & \\ & & O & & \\ & O & & O & \\ O & & & & O \\ \end{tabular}
Proposed by David Tang