8 checkers' game in 1x8 board
Source: VII May Olympiad (Olimpiada de Mayo) 2001 L1 P5
September 22, 2022
gamecombinatoricsgame strategy
Problem Statement
In an -square board -like the one in the figure- there is initially one checker in each square.
\begin{tabular}{ | l | c | c |c | c| c | c | c | r| }
\hline
& & & & & & & \\ \hline
\end{tabular}
A move consists of choosing two tokens and moving one of them one square to the right and the other one one square to the left. If after moves the checkers are distributed in only boxes, determine what those boxes can be and how many checkers are in each one.