Arrays of numbers

Problem :

Prove that among any 10 entries of the table:

$\begin{tabular}{cccccccccc} 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ 9 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ 8 & 9 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ 7 & 8 & 9 & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ 6 & 7 & 8 & 9 & 0 & 1 & 2 & 3 & 4 & 5 \\ 5 & 6 & 7 & 8 & 9 & 0 & 1 & 2 & 3 & 4 \\ 4 & 5 & 6 & 7 & 8 & 9 & 0 & 1 & 2 & 3 \\ 3 & 4 & 5 & 6 & 7 & 8 & 9 & 0 & 1 & 2 \\ 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 0 & 1 \\ 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 0 \end{tabular}$

situated in different rows and different columns, at least two are equal.

Please send your comments, solutions…most welcome 🙂

more later,

Nalin Pithwa

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