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The letters $A, B$ and $C$ are used to form every possible three letter ``word.'' When these ``words'' are arranged in alphabetical order and numbered so that $AAA$ is Word 1 and $CCC$ is Word 27, what number will correspond to the position of word $BAB$ on the list?

 May 28, 2021
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There is probably a smart way of doing this, but I'm just going to list the 27 "words."

 

1. AAA

2. AAB

3. AAC

4. ABA

5. ABB

6. ABC

7. ACA

8. ACB

9. ACC

10. BAA

11. BAB

 

So the answer is 11.

I guess the "smart" way of doing this is recognizing that numbers 1-9 start with A, 10-18 start with B, and 19-27 start with C. BAB is the 2nd word that starts with B, so 9+2=11.

Nice problem!

 May 28, 2021

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