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The october 13, 2006 exam for the combinatorics course, math 0345. The exam covers various topics including magic squares, simple graphs, combinations, and the binomial theorem. Questions include proving identities, using combinatorial reasoning, and expanding expressions using the binomial theorem.
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Name: Honor Code Pledge
Signature Directions: Please complete all but 1 problem. There is a time limit of 2 hours.
k+ ︷ ︸︸ ︷ 3 , 3 ,... 3) ≤ (k + 1)(r(
k ︷ ︸︸ ︷ 3 , 3 ,... 3) − 1) + 2.
z 1 + z 2 + z 3 = 11 if z 1 ≥ 2 and z 2 > z 3.
( n k
n − 3 k
n − 1 k − 1
n − 2 k − 1
n − 3 k − 1
(Hint: Let S be a set with three distinguished elements a, b and x and count certain k-combinations of S.)