Editorial for COCI '06 Contest 4 #1 Sibice

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Since the box is of rectangular shape, the longest possible match is the same length as the diagonal of the box. A match fits in the box if $W^2 + H^2 \ge L^2$ ~W^2 + H^2 \ge L^2~, where $L$ ~L~ is the length of the match.

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