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# Counting problem

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In how many ways can you change a 20 dollar bill using 10 dollar bills, 5 dollar bills, 2 dollar bills, and 1 dollar bills?

Dec 27, 2021

#1
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n     \$1 \$2 \$5 \$10

1  = (20, 0, 0, 0)
2  = (18, 1, 0, 0)
3  = (16, 2, 0, 0)
4  = (14, 3, 0, 0)
5  = (12, 4, 0, 0)
6  = (10, 5, 0, 0)
7  = (8, 6, 0, 0)
8  = (6, 7, 0, 0)
9  = (4, 8, 0, 0)
10  = (2, 9, 0, 0)
11  = (0, 10, 0, 0)
12  = (15, 0, 1, 0)
13  = (13, 1, 1, 0)
14  = (11, 2, 1, 0)
15  = (9, 3, 1, 0)
16  = (7, 4, 1, 0)
17  = (5, 5, 1, 0)
18  = (3, 6, 1, 0)
19  = (1, 7, 1, 0)
20  = (10, 0, 2, 0)
21  = (8, 1, 2, 0)
22  = (6, 2, 2, 0)
23  = (4, 3, 2, 0)
24  = (2, 4, 2, 0)
25  = (0, 5, 2, 0)
26  = (5, 0, 3, 0)
27  = (3, 1, 3, 0)
28  = (1, 2, 3, 0)
29  = (0, 0, 4, 0)
30  = (10, 0, 0, 1)
31  = (8, 1, 0, 1)
32  = (6, 2, 0, 1)
33  = (4, 3, 0, 1)
34  = (2, 4, 0, 1)
35  = (0, 5, 0, 1)
36  = (5, 0, 1, 1)
37  = (3, 1, 1, 1)
38  = (1, 2, 1, 1)
39  = (0, 0, 2, 1)
40  = (0, 0, 0, 2)

40 ways to make a change for a \$20 bill.

Dec 27, 2021