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Found problems: 1

2007 District Olympiad, 2
Tags: rectangle , counting , combinatorics , numbering , geometry
All $ 2n\ge 2 $ squares of a $ 2\times n $ rectangle are colored with three colors. We say that a color has a [i]cut[/i] if there is some column (from all $ n $) that has both squares colored with it. Determine: [b]a)[/b] the number of colorings that have no cuts. [b]b)[/b] the number of colorings that have a single cut.