TheIceBerg
New member
- Joined
- Dec 2, 2018
- Messages
- 1
Hello,
Imagine I have a pile of bills in the following denominations: $1, $2 and $3. How many ways can I make exactly $10 using these bills? Let's assume I have more than enough of each bill to make $10. I have come up with 14 ways just by listing them, but want to make sure I am not missing any. If the raw mathematics of it are digestible to a layperson, the "shortcut" would be appreciated as well in case I need to do this again with different values. Here are the solutions I have found so far:
10 $1
8 $1 and 1 $2
7 $1 and 1 $3
6 $1 and 2 $2
5 $1, 1 $2 and 1 $3
4 $1 and 3 $2
4 $1 and 2 $3
3 $1, 2 $2 and 1 $3
2 $1 and 4 $2
2 $1, 1 $2 and 2 $3
1 $1, 3 $2 and 1 $3
1 $1 and 3 $3
5 $2
2 $2 and 2 $3
Is that all of the possibilities? Is there a quick way to check? Any help would be appreciated.
Imagine I have a pile of bills in the following denominations: $1, $2 and $3. How many ways can I make exactly $10 using these bills? Let's assume I have more than enough of each bill to make $10. I have come up with 14 ways just by listing them, but want to make sure I am not missing any. If the raw mathematics of it are digestible to a layperson, the "shortcut" would be appreciated as well in case I need to do this again with different values. Here are the solutions I have found so far:
10 $1
8 $1 and 1 $2
7 $1 and 1 $3
6 $1 and 2 $2
5 $1, 1 $2 and 1 $3
4 $1 and 3 $2
4 $1 and 2 $3
3 $1, 2 $2 and 1 $3
2 $1 and 4 $2
2 $1, 1 $2 and 2 $3
1 $1, 3 $2 and 1 $3
1 $1 and 3 $3
5 $2
2 $2 and 2 $3
Is that all of the possibilities? Is there a quick way to check? Any help would be appreciated.