S15 Exam 2 Problem 1
[Reserved for Score]
III mil III
Combinatorics, Dave Bayer
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Exam 01
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[1] Up to rotational symmetry, how many nine bead necklaces have three red beads and six blue beads?
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S15 Exam 2 Problem 2
[Reserved for Score]
I III IIII III
Combinatorics, Dave Bayer
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Exam 01
[2] Up to symmetry (rotations and flips), how^ many ways can the squares of a 4 by 4 checkerboard be
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S15 Exam 2 Problem 3
[Reserved for Score]
IIIIIIII III
Combinatorics, Dave Bayer
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Exam 01
[3] Up to rotational symmetry, how many ways can the eight corners of a cube be colored using n colors?
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S15 Exam 2 Problem 4
[Reserved for Score]
Combinatorics, Dave Bayer
exam01a2p4
Exam 01
[4] Give a proof of Burnside's Lemma: If a group G acts on a set of patterns X, then the number of distinct
patterns up to symmetry is equal to the average number of patterns fixed by an element of the group;
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