How many ways can you have $1.05 with only dimes, nickels, and quarters?

Question

Any ideas?

Answer 1

I'm going to go with 31 ways...

Nickels (1):
21 nickels

Nickels and dimes (10):
19 nickels and 1 dime
17 nickels and 2 dimes
15 nickels and 3 dimes
13 nickels and 4 dimes
11 nickels and 5 dimes
9 nickels and 6 dimes
7 nickels and 7 dimes
5 nickels and 8 dimes
3 nickels and 9 dimes
1 nickel and 10 dimes

Nickels and quarters (4):
1 nickel and 4 quarters
6 nickels and 3 quarters
11 nickels and 2 quarters
16 nickels and 1 quarters

Quarters and dimes (2):
1 quarter 8 dimes
3 quarters 3 dimes

Quarters dimes and nickels (14):
1 quarter 1 dime 14 nickels
1 quarter 2 dimes 12 nickels
1 quarter 3 dimes 10 nickels
1 quarter 4 dimes 8 nickels
1 quarter 5 dimes 6 nickels
1 quarter 6 dimes 4 nickels
1 quarter 7 dimes 2 nickels

2 quarters 1 dime 9 nickels
2 quarters 2 dimes 7 nickels
2 quarters 3 dimes 5 nickels
2 quarters 4 dimes 3 nickels
2 quarters 5 dimes 1 nickels

3 quarters 1 dime 4 nickels
3 quarters 2 dimes 2 nickels

Answer 2

Well.. let's see.. how about 31.

1. 4q, 1n
2. 3q, 3d
3. 3q, 2d, 2n
4. 3q, 1d, 4n
5. 3q, 6n
6, 2q, 5d, 1n
7. 2q, 4d, 3n
8. 2q, 3d, 5n
9. 2q, 2d, 7n
10. 2q, 1d, 9n
11. 2q, 11n
12. 1q, 8d
13. 1q, 7d, 2n
14. 1q, 6d, 4n
15. 1q, 5d, 6n
16. 1q, 4d, 8n
17. 1q, 3d, 10n
18. 1q, 2d, 12n
19. 1q, 1d, 14n
20. 1q, 16n
21. 10d, 1n
22. 9d, 3n
23. 8d, 5n
24. 7d, 7n
25. 6d, 9n
26. 5d, 11n
27. 4d, 13n
28. 3d, 15n
29. 2d, 17n
30. 1d, 19n
31. 21n

There's probably a math formula.. but this was more fun!

Hope this helps!