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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?
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