Unformatted text preview: j Orb( x ) j = j G j = j Stab( x ) j for each x 2 X . (This veri±es the result of Theorem 5.4.3 (OrbitStabilizer Theorem) in this case.) 4. (a) Find the number of di²erent squares with vertices colored red, white, or blue. (b) Find the number of di²erent mcolored squares for any m . 5. A wheel is divided evenly into six di²erent compartments. Each compartment can be painted red or white. The back of the wheel is black. How many di²erent color wheels are there? 6. A rectangular design consists of 10 parallel stripes of equal width. If each stripe can be painted red, blue, or green, ±nd the number of possible patterns. 7. Each side of an equilateral triangle is divided into two equal parts, and each part is colored red, yellow, or green. Find the number of patterns. Math 4023 1...
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 Fall '09

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