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?

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?

What Information Do We Have?

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

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?

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

What Could We List?

Ways to make $1 with quarters, dimes, and nickels.

OR

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

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

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

• We counted 13 possibilities• The question asks “how many ways”• We know we haven’t repeated any

possibilities because of the columns• We know we’ve tried all the

combinations because we went in order• So YES we can answer the question

Can We Answer the Question?