List all coin combinations you could use to make 78 cents.?

Question

I need this for my homework

Answer 1

combinations: 134
This includes half-dollars (h), but there are only 13 combinations involving at least one half-dollar (leaving 121 combinations if you don't use them).

No quarters:
[78p] [1n73p] [2n68p] [3n63p] [4n58p] [5n53p] [6n48p] [7n43p] [8n38p] [9n33p] [10n28p] [11n23p] [12n18p] [13n13p] [14n8p] [15n3p] [1d68p] [1d1n63p] [1d2n58p] [1d3n53p] [1d4n48p] [1d5n43p] [1d6n38p] [1d7n33p] [1d8n28p] [1d9n23p] [1d10n18p] [1d11n13p] [1d12n8p] [1d13n3p] [2d58p] [2d1n53p] [2d2n48p] [2d3n43p] [2d4n38p] [2d5n33p] [2d6n28p] [2d7n23p] [2d8n18p] [2d9n13p] [2d10n8p] [2d11n3p] [3d48p] [3d1n43p] [3d2n38p] [3d3n33p] [3d4n28p] [3d5n23p] [3d6n18p] [3d7n13p] [3d8n8p] [3d9n3p] [4d38p] [4d1n33p] [4d2n28p] [4d3n23p] [4d4n18p] [4d5n13p] [4d6n8p] [4d7n3p] [5d28p] [5d1n23p] [5d2n18p] [5d3n13p] [5d4n8p] [5d5n3p] [6d18p] [6d1n13p] [6d2n8p] [6d3n3p] [7d8p] [7d1n3p]

One quarter:
[1q53p] [1q1n48p] [1q2n43p] [1q3n38p] [1q4n33p] [1q5n28p] [1q6n23p] [1q7n18p] [1q8n13p] [1q9n8p] [1q10n3p] [1q1d43p] [1q1d1n38p] [1q1d2n33p] [1q1d3n28p] [1q1d4n23p] [1q1d5n18p] [1q1d6n13p] [1q1d7n8p] [1q1d8n3p] [1q2d33p] [1q2d1n28p] [1q2d2n23p] [1q2d3n18p] [1q2d4n13p] [1q2d5n8p] [1q2d6n3p] [1q3d23p] [1q3d1n18p] [1q3d2n13p] [1q3d3n8p] [1q3d4n3p] [1q4d13p] [1q4d1n8p] [1q4d2n3p] [1q5d3p]

Two quarters:
[2q28p] [2q1n23p] [2q2n18p] [2q3n13p] [2q4n8p] [2q5n3p] [2q1d18p] [2q1d1n13p] [2q1d2n8p] [2q1d3n3p] [2q2d8p] [2q2d1n3p]

Three quarters:
[3q3p]

One half-dollar:
[1h28p] [1h1n23p] [1h2n18p] [1h3n13p] [1h4n8p] [1h5n3p] [1h1d18p] [1h1d1n13p] [1h1d2n8p] [1h1d3n3p] [1h2d8p] [1h2d1n3p]

One half-dollar AND one quarter:
[1h1q3p]

=======
Courtesy of this Java program:

int printed = 0;
final int cents=78;
for (int h=0; h<=cents/50; ++h) {
for (int q=0; q<=(cents-50*h)/25; ++q) {
for (int d=0; d<=(cents-50*h-25*q)/10; ++d) {
for (int n=0; n<=(cents-50*h-25*q-10*d)/5; ++n) {
int p = cents - 50*h - 25*q - 10*d - 5*n;
if (p >= 0) {
++printed;
System.out.print("[" + ((h==0)? "" : h + "h") + ((q==0) ? "" : q + "q") + ((d==0) ? "" : d + "d") + ((n==0) ? "" : n + "n") + p + "p] ");
} } } } }
System.out.println();
System.out.println( "combinations: " + printed);

Answer 2

I notice someone mentions 1/2 cent. If those are included, you need to consider 2 cent and 3 cent coins as well as twenty cent coins.
Apparantly the 1/2 cent answer disappeared.

Answer 3

P = penny, N = nickel, D = dime, Q = quarter, H = half dollar

78P
73P 1N
68P 1D
68P 2N
63P 1D 1N
63P 3N
58P 2D
58P 1D 2N
58P 4N
53P 1Q
53P 2D 1N
53P 1D 3N
53P 5N
48P 1Q 1N
48P 2D 2N
48P 1D 4N
48P 6N
43P 1Q 1D
43P 1Q 2N
43P 3D 1N
43P 2D 3N
43P 1D 5N
43P 7N
38P 1Q 1D 1N
38P 1Q 3N
38P 4D
38P 3D 2N
38P 2D 4N
38P 1D 6N
38P 8N
33P 1Q 2D
33P 1Q 1D 2N
33P 1Q 4N
33P 4D 1N
33P 3D 3N
33P 2D 5N
33P 1D 7N
33P 9N
28P 1H
28P 2Q
28P 1Q 2D 1N
28P 1Q 1D 3N
28P 1Q 5N
28P 5D
28P 4D 2N
28P 3D 4N
28P 2D 6N
28P 1D 8N
28P 10N
23P 1H 1N
23P 2Q 1N
23P 1Q 3D
23P 1Q 2D 2N
23P 1Q 1D 4N
23P 1Q 6N
23P 5D 1N
23P 4D 3N
23P 3D 5N
23P 2D 7N
23P 1D 9N
23P 11N
18P 1H 1D
18P 1H 2N
18P 2Q 1D
18P 2Q 2N
18P 1Q 3D 1N
18P 1Q 2D 3N
18P 1Q 1D 5N
18P 1Q 7N
18P 6D
18P 5D 2N
18P 4D 4N
18P 3D 6N
18P 2D 8N
18P 1D 10N
18P 12N
13P 1H 1D 1N
13P 1H 3N
13P 2Q 1D 1N
13P 2Q 3N
13P 1Q 4D
13P 1Q 3D 2N
13P 1Q 2D 4N
13P 1Q 1D 6N
13P 1Q 8N
13P 6D 1N
13P 5D 3N
13P 4D 5N
13P 3D 7N
13P 2D 9N
13P 1D 11N
13P 13N
8P 1H 2D
8P 1H 1D 2N
8P 1H 4N
8P 2Q 2D
8P 2Q 1D 2N
8P 2Q 4N
8P 1Q 4D 1N
8P 1Q 3D 3N
8P 1Q 2D 5N
8P 1Q 1D 7N
8P 1Q 9N
8P 7D
8P 6D 2N
8P 5D 4N
8P 4D 6N
8P 3D 8N
8P 2D 10N
8P 1D 12N
8P 14N
3P 1H 1Q
3P 1H 2D 1N
3P 1H 1D 3N
3P 1H 5N
3P 3Q
3P 2Q 2D 1N
3P 2Q 1D 3N
3P 2Q 5N
3P 1Q 5D
3P 1Q 4D 2N
3P 1Q 3D 4N
3P 1Q 2D 6N
3P 1Q 1D 8N
3P 1Q 10N
3P 7D 1N
3P 6D 3N
3P 5D 5N
3P 4D 7N
3P 3D 9N
3P 2D 11N
3P 1D 13N
3P 15N

Answer 4

way too many.

Answer 5

p=pennies
n=nickels
d=dimes
q=quarters
h=half dollars

78p
73p1n
68p2n
68p1d
63p3n
63p1n1d
58p4n
58p2n1d
58p2d
53p5n
53p3n1d
53p1n2d
53p1q
48p6n
48p4n1d
48p2n2d
48p1n1q
48p3d
43p7n
43p5n1d
43p3n2d
43p2n1q
43p1n3d
38p8n
38p6n1d
38p4n2d
38p3n1q
38p2n3d
38p1n1d1q
38p4d


etc