MathDB

Let

n\ge 3

be an integer. Put

n^2

cards, each labelled

1,2,\ldots ,n^2

respectively, in any order into

n

empty boxes such that there are exactly

n

cards in each box. One can perform the following operation: one first selects

2

boxes, takes out any

2

cards from each of the selected boxes, and then return the cards to the other selected box. Prove that, for any initial order of the

n^2

cards in the boxes, one can perform the operation finitely many times such that the labelled numbers in each box are consecutive integers.

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