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# in how many different ways can you make change for a dollar

Customer Question
? Show work and explain...
in how many different ways can you make change for a dollar ? Show work and explain. Also I can only use pennies, nicketls, dimes, and quarters
Submitted: 6 years ago.Category: General
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12/7/2010
Expert: General Jay, Problem Solver replied 6 years ago
General Jay, Problem Solver
Category: General
Satisfied Customers: 1,053
Experience: General contractor, project manager, excellent problem solving skills, retired professional athlete.
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There are 226 different ways to make change for a dollar using only pennies, nickels, dimes and quarters. See breakdown below.

P - N - D - Q
100 - 0 - 0 - 0
95 - 1 - 0 - 0
90 - 2 - 0 - 0
90 - 0 - 1 - 0
85 - 3 - 0 - 0
85 - 1 - 1 - 0
80 - 4 - 0 - 0
80 - 2 - 1 - 0
80 - 0 - 2 - 0
75 - 5 - 0 - 0
75 - 3 - 1 - 0
75 - 1 - 2 - 0
75 - 0 - 0 - 1
70 - 6 - 0 - 0
70 - 4 - 1 - 0
70 - 2 - 2 - 0
70 - 1 - 0 - 1
65 - 7 - 0 - 0
65 - 5 - 1 - 0
65 - 3 - 2 - 0
65 - 2 - 0 - 1
65 - 1 - 3 - 0
65 - 0 - 1 - 1
60 - 8 - 0 - 0
60 - 6 - 1 - 0
60 - 4 - 2 - 0
60 - 3 - 0 - 1
60 - 2 - 3 - 0
60 - 1 - 1 - 1
60 - 0 - 4 - 0
55 - 9 - 0 - 0
55 - 7 - 1 - 0
55 - 5 - 2 - 0
55 - 4 - 0 - 1
55 - 3 - 3 - 0
55 - 2 - 1 - 1
55 - 1 - 4 - 0
55 - 0 - 2 - 1
50 - 10 - 0 - 0
50 - 8 - 1 - 0
50 - 6 - 2 - 0
50 - 5 - 0 - 1
50 - 4 - 3 - 0
50 - 3 - 1 - 1
50 - 2 - 4 - 0
50 - 1 - 2 - 1
50 - 0 - 0 - 2
45 - 11 - 0 - 0
45 - 9 - 1 - 0
45 - 7 - 2 - 0
45 - 6 - 0 - 1
45 - 5 - 3 - 0
45 - 3 - 4 - 0
45 - 2 - 2 - 1
45 - 1 - 5 - 0
45 - 1 - 0 - 2
45 - 0 - 3 - 1
40 - 12 - 0 - 0
40 - 10 - 1 - 0
40 - 8 - 2 - 0
40 - 7 - 0 - 1
40 - 6 - 3 - 0
40 - 5 - 1 - 1
40 - 4 - 4 - 0
40 - 3 - 2 - 1
40 - 2 - 5 - 0
40 - 2 - 0 - 2
40 - 1 - 3 - 1
40 - 0 - 6 - 0
40 - 0 - 1 - 2
35 - 13 - 0 - 0
35 - 11 - 1 - 0
35 - 9 - 2 - 0
35 - 8 - 0 - 1
35 - 7 - 3 - 0
35 - 6 - 1 - 1
35 - 5 - 4 - 0
35 - 4 - 2 - 1
35 - 3 - 5 - 0
35 - 3 - 0 - 2
35 - 2 - 3 - 1
35 - 1 - 6 - 0
35 - 1 - 1 - 2
35 - 0 - 4 - 1
30 - 14 - 0 - 0
30 - 12 - 1 - 0
30 - 10 - 2 - 0
30 - 9 - 0 - 1
30 - 8 - 3 - 0
30 - 7 - 1 - 1
30 - 6 - 4 - 0
30 - 5 - 2 - 1
30 - 4 - 5 - 0
30 - 4 - 0 - 2
30 - 3 - 3 - 1
30 - 2 - 6 - 0
30 - 2 - 1 - 2
30 - 1 - 4 - 1
30 - 0 - 7 - 0
25 - 15 - 0 - 0
25 - 13 - 1 - 0
25 - 11 - 2 - 0
25 - 10 - 0 - 1
25 - 9 - 3 - 0
25 - 8 - 1 - 1
25 - 7 - 4 - 0
25 - 6 - 2 - 1
25 - 5 - 5 - 0
25 - 5 - 0 - 2
25 - 4 - 3 - 1
25 - 3 - 6 - 0
25 - 2 - 4 - 1
25 - 1 - 7 - 0
25 - 1 - 2 - 2
25 - 0 - 0 - 3
20 - 16 - 0 - 0
20 - 14 - 1 - 0
20 - 12 - 2 - 0
20 - 11 - 0 - 1
20 - 10 - 3 - 0
20 - 9 - 1 - 1
20 - 8 - 4 - 0
20 - 7 - 2 - 1
20 - 6 - 5 - 0
20 - 6 - 0 - 2
20 - 5 - 3 - 1
20 - 4 - 6 - 0
20 - 4 - 1 - 2
20 - 3 - 4 - 1
20 - 2 - 2 - 2
20 - 1 - 0 - 3
20 - 0 - 8 - 0
15 - 17 - 0 - 0
15 - 15 - 1 - 0
15 - 13 - 2 - 0
15 - 12 - 0 - 1
15 - 11 - 3 - 0
15 - 10 - 1 - 1
15 - 9 - 4 - 0
15 - 8 - 2 - 1
15 - 7 - 5 - 0
15 - 7 - 0 - 2
15 - 6 - 3 - 1
15 - 5 - 6 - 0
15 - 5 - 1 - 2
15 - 4 - 4 - 1
15 - 3 - 7 - 0
15 - 3 - 2 - 2
15 - 2 - 0 - 3
15 - 2 - 5 - 1
15 - 1 - 8 - 0
15 - 0 - 6 - 1
15 - 0 - 1 - 3
10 - 18 - 0 - 0
10 - 16 - 1 - 0
10 - 14 - 2 - 0
10 - 13 - 0 - 1
10 - 12 - 3 - 0
10 - 11 - 1 - 1
10 - 10 - 4 - 0
10 - 9 - 2 - 1
10 - 8 - 5 - 0
10 - 8 - 0 - 2
10 - 7 - 3 - 1
10 - 6 - 6 - 0
10 - 6 - 1 - 2
10 - 5 - 4 - 1
10 - 4 - 7 - 0
10 - 4 - 2 - 2
10 - 3 - 0 - 3
10 - 3 - 5 - 1
10 - 2 - 8 - 0
10 - 2 - 3 - 2
10 - 1 - 1 - 3
10 - 1 - 6 - 1
10 - 0 - 9 - 0
10 - 0 - 4 - 2
5 - 19 - 0 - 0
5 - 17 - 1 - 0
5 - 15 - 2 - 0
5 - 14 - 0 - 1
5 - 13 - 3 - 0
5 - 12 - 1 - 1
5 - 11 - 4 - 0
5 - 10 - 2 - 1
5 - 9 - 5 - 0
5 - 9 - 0 - 2
5 - 8 - 3 - 1
5 - 7 - 6 - 0
5 - 7 - 1 - 2
5 - 6 - 4 - 1
5 - 5 - 7 - 0
5 - 5 - 2 - 2
5 - 4 - 0 - 3
5 - 4 - 5 - 1
5 - 3 - 8 - 0
5 - 2 - 6 - 1
5 - 2 - 1 - 3
5 - 1 - 9 - 0
5 - 1 - 4 - 2
5 - 0 - 7 - 1
5 - 0 - 2 - 3
0 - 20 - 0 - 0
0 - 18 - 1 - 0
0 - 16 - 2 - 0
0 - 15 - 0 - 1
0 - 14 - 3 - 0
0 - 13 - 1 - 1
0 - 12 - 4 - 0
0 - 11 - 2 - 1
0 - 10 - 5 - 0
0 - 10 - 0 - 2
0 - 9 - 3 - 1
0 - 8 - 6 - 0
0 - 8 - 1 - 2
0 - 7 - 4 - 1
0 - 6 - 7 - 0
0 - 6 - 2 - 2
0 - 5 - 0 - 3
0 - 4 - 8 - 0
0 - 4 - 3 - 2
0 - 3 - 1 - 3
0 - 3 - 6 - 1
0 - 0 - 10 - 0
0 - 0 - 5 - 2
0 - 0 - 0 - 4

General Jay, Problem Solver
Category: General
Satisfied Customers: 1,053
Experience: General contractor, project manager, excellent problem solving skills, retired professional athlete.
Verified
Customer reply replied 6 years ago
how did you arrive in this answer? It's great!!! but I can't figure out how you did it
Customer reply replied 6 years ago
Did you get my second question?
Expert: General Jay, Problem Solver replied 6 years ago

I started with 100 pennies equalling a dollar. I worked backwards from 100 in increments of 5 pennies because nickels, dimes and quarters are all divisible by 5. For example, you cannot have 99 pennies and use a nickel, dime or a quarter to equal one dollar.

If you have 95 pennies, then only a nickel can be used to equal a dollar and so on.....it was tedious, but I wrote them down in columns.

General Jay, Problem Solver
Category: General
Satisfied Customers: 1,053
Experience: General contractor, project manager, excellent problem solving skills, retired professional athlete.
Verified
Customer reply replied 6 years ago
can you send me the spread sheet you did this on. I'm trying to duplicate it. . also I counted a total of 233 iterations. Which7 did you eliminate? thanks
Customer reply replied 6 years ago
can I call you? I will pay of course?
General Jay, Problem Solver
Category: General
Satisfied Customers: 1,053
1,053 Satisfied Customers
Experience: General contractor, project manager, excellent problem solving skills, retired professional athlete.

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