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Bicycle license plates in Flatville each contain three letters. The first is chosen from the set $\{C,H,L,P,R\},$ the second from $\{A,I,O\},$ and the third from $\{D,M,N,T\}.$

When Flatville needed more license plates, they added two new letters. The new letters may both be added to one set or one letter may be added to one set and one to another set. What is the largest possible number of ADDITIONAL license plates that can be made by adding two letters?

 Jun 14, 2023
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The original number of license plates is 534 = 60.

If both new letters are added to the same set, the number of additional license plates is 234 = 24.

If one new letter is added to each set, the number of additional license plates is 232 = 12.

The largest possible number of additional license plates is 24, so the answer is 24.

 Jun 14, 2023

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