98363 – We Solve Problems

Problem № 98363 10-13

Initially, on each cell of a $1 × n$ board a checker is placed. The first move allows you to move any checker onto an adjacent cell $($one of the two, if the checker is not on the edge$)$, so that a column of two pieces is formed. Then one can move each column in any direction by as many cells as there are checkers in it $($within the board$)$; if the column is on a non-empty cell, it is placed on a column standing there and unites with it. Prove that in  $n – 1$ moves you can collect all of the checkers on one square.

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