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Carla has 10 coins, each of which is a nickel, a dime, or a quarter, or a penny. The total value of her coins is less than $1.00. How many different combinations of coins might Carla have?

 Jun 14, 2022
 #1
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My computer says this many sums:

 

        p  n  d  q

1  = (7, 1, 1, 1) == 47
2  = (6, 2, 1, 1) == 51
3  = (5, 3, 1, 1) == 55
4  = (4, 4, 1, 1) == 59
5  = (3, 5, 1, 1) == 63
6  = (2, 6, 1, 1) == 67
7  = (1, 7, 1, 1) == 71
8  = (6, 1, 2, 1) == 56
9  = (5, 2, 2, 1) == 60
10  = (4, 3, 2, 1) == 64
11  = (3, 4, 2, 1) == 68
12  = (2, 5, 2, 1) == 72
13  = (1, 6, 2, 1) == 76
14  = (5, 1, 3, 1) == 65
15  = (4, 2, 3, 1) == 69
16  = (3, 3, 3, 1) == 73
17  = (2, 4, 3, 1) == 77
18  = (1, 5, 3, 1) == 81
19  = (4, 1, 4, 1) == 74
20  = (3, 2, 4, 1) == 78
21  = (2, 3, 4, 1) == 82
22  = (1, 4, 4, 1) == 86
23  = (3, 1, 5, 1) == 83
24  = (2, 2, 5, 1) == 87
25  = (1, 3, 5, 1) == 91
26  = (2, 1, 6, 1) == 92
27  = (1, 2, 6, 1) == 96
28  = (6, 1, 1, 2) == 71
29  = (5, 2, 1, 2) == 75
30  = (4, 3, 1, 2) == 79
31  = (3, 4, 1, 2) == 83
32  = (2, 5, 1, 2) == 87
33  = (1, 6, 1, 2) == 91
34  = (5, 1, 2, 2) == 80
35  = (4, 2, 2, 2) == 84
36  = (3, 3, 2, 2) == 88
37  = (2, 4, 2, 2) == 92
38  = (1, 5, 2, 2) == 96
39  = (4, 1, 3, 2) == 89
40  = (3, 2, 3, 2) == 93
41  = (2, 3, 3, 2) == 97
42  = (3, 1, 4, 2) == 98
43  = (5, 1, 1, 3) == 95
44  = (4, 2, 1, 3) == 99

 Jun 14, 2022

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