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Home » Thus, the smallest such number is $\boxed120$. - Upplift

Thus, the smallest such number is $\boxed120$. - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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Determine positions for the A's:
Once the non-A letters are arranged, they create 5 possible "gaps" whe...
For example, for arrangement B C C D, the gaps are:
\_\, B \_\, C \_\, C \_\, D \_
We need to place 2 identical A's into these 5 gaps, with at most one A...
Choose 2 distinct gaps out of 5:
The number of ways to choose 2 distinct gaps is:
Compute total valid sequences:
Each arrangement of the non-A letters allows 10 ways to place the A's...
Therefore, the total number of valid sequences is:

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