The Tooth Fairy Problem

1
The Tooth Fairy Problem

• The tooth fairy is giving children 1 for each
  tooth lost this month. The tooth fairy has only
  quarters, dimes, and nickels to give away. If the
  tooth fairy must use at least one of each coin,
  how many ways can the 1 be made?

2
What Is the Question We Are Asked?

• The tooth fairy is giving children 1 for each
  tooth lost this month. The tooth fairy has only
  quarters, dimes, and nickels to give away. If the
  tooth fairy must use at least one of each coin,

how many ways can the 1 be made?
3
What Information Do We Have?

• The tooth fairy is giving children 1 for each
  tooth lost this month. The tooth fairy has only
  quarters, dimes, and nickels to give away. If the
  tooth fairy must use at least one of each coin,
  how many ways can the 1 be made?

• 1 for each tooth
• Only quarters, nickels and dimes
• Must use at least one of each coin

4
What Information Are We Looking For?

• The tooth fairy is giving children 1 for each
  tooth lost this month. The tooth fairy has only
  quarters, dimes, and nickels to give away. If the
  tooth fairy must use at least one of each coin,
  how many ways can the 1 be made?

• Combinations that make 1 AND
• that use one of each coin AND
• a list of ALL possible combinations

5
What Could We List?
Ways to make 1 with quarters, dimes, and nickels.
OR
6
How Will We Know If We Repeat a Combination?
Always put the coins in the same order.
2 4
2 3 2
1 3
1 3 2
4 2 1
6
3
7
How Will We Know When We Are Finished?
Use a system to try all combinations for one
coin, then another, etc.
3 2
1 3
1 3 2
4
2 2 3
4 2
2 6 2
1
8
8
Count All The Possibilities
3 2
1 3
1 3 2
4
2 2 3
4 2
2 6 2
1
8 1 7
1 1
6 3
1 5
5 1 4
7 1
3 9
1 2
11 1
1 13
9
Can We Answer the Question?

• We counted 13 possibilities
• The question asks how many ways
• We know we havent repeated any possibilities
  because of the columns
• We know weve tried all the combinations because
  we went in order
• So YES we can answer the question