Unformatted text preview: B \ { k }} and use the inclusionexclusion formula. 5. 100 people are at a party. Each has an even number of aquaintances (possibly 0). Show that there are at least three persons having the same number of acquaintances in the group. 6. Let A = { 1 , . . . , n } . Compute the number of maps f : A ±→ A without a ﬁxed point ( f ( i ) ² = i, ∀ i = 1 , . . . , n ) . 7. Let a 1 , a 2 , . . . , a n be n given integers not necessarily distinct. Show that there exist integers k, l with 0 ≤ k < l ≤ n such that a k +1 + a k +2 + a l is a multiple of n. Hint: consider the sums S i = ∑ i j =1 a j , i ≤ n . 1...
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This homework help was uploaded on 04/08/2008 for the course MATH 145 taught by Professor Peche during the Spring '07 term at UC Davis.
 Spring '07
 Peche
 Math, Combinatorics

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