The sequence is "333xxxxx". The fourth digit cannot be 3 (to avoid "3333"), so it must be 4. The remaining 4 digits can be either 3 or 4, giving \(2^4 = 16\) configurations.

February 22, 2026

$The sequence is "333xxxxx". The fourth digit cannot be 3 (to avoid "3333"), so it must be 4. The remaining 4 digits can be either 3 or 4, giving \(2^4 = 16\) configurations.$

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After placing "333", we have 5 positions left. Each of these can be either a 3 or a 4, except that no additional block of three consecutive 3's is allowed. We need to ensure that no new block of three consecutive 3's is formed.
Count valid configurations for each block position:
If "333" starts at position 1:
If "333" starts at position 2:
The sequence is "x333xxxx". The first digit can be 3 or 4 (2 choices), and the fifth digit must be 4 to avoid "3333". The last 3 digits can be either 3 or 4, giving \(2 \times 2^3 = 16\) configurations.
If "333" starts at position 3:

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