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\begin{document}


\begin{center}
\bigskip {\Large Puzzle 2 - SOLUTION}
\end{center}

\bigskip

\begin{problem}
Consider a chess board with two corners missing, as indicated on the picture
below. We also have $31$ pieces of domino, each of them can cover exactly $2$
fields on the chess board. Is it possible to cover the chessboard with the
domino pieces?
\end{problem}

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\begin{solution}
The solution boils down to coloring. No matter how place a domino, it will
always cover exactly one white and one black field. The original chess board
had $32$ white and $32$ black fields. Since the two corners missing are both
black, now we need to cover $32$ white and $30$ black fields with $31$
dominos. This is onviously impossible.
\end{solution}

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