# Solving Discrete Mathematics Questions

1. After a weekend at the Mohegan Sun Casino, Gary finds that he has won $1020—in $20 and $50 chips. If he has more $50 chips than $20 chips, how many chips of each denomination could he possibly have?

2. If there are 2187 functions f : A→B and |B| = 3, what is |A|?

3. Let A ⊆ {1, 2, 3, . . . , 25} where |A| = 9. For any subset of A let sB denote the sum of the elements in B. Prove that there are distinct subsets C, D of A such that |C| = |D| = 5 and sC = sD.

4. Let g: N→N be defined by g(n) = 2n. If A ={1, 2, 3, 4} and f : A→N is given by f _ {(1, 2), (2, 3), (3, 5), (4, 7)}, find g ◦ f .

5. Let a1, a2, a3, . . . be the integer sequence defined recursively by

a. a1 =0; and

b. For n > 1, an = + a[n/2].

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1. After a weekend at the Mohegan Sun Casino, Gary finds that he has won $1020—in $20 and $50 chips. If he has more $50 chips than $20 chips, how many chips of each denomination could he possibly have?

$50 Chip $20 Chip

Number 20 1

Number 18 6

Number 16 11

So there are 3 possible combinations shown as above.

2. If there are 2187 ...

#### Solution Summary

The solution gives detailed steps on solving several questions on discrete mathematics.