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Home » However, in olympiad problems, such divisions are accepted if calculated precisely - Abbey Badges

However, in olympiad problems, such divisions are accepted if calculated precisely - Abbey Badges

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📝 Recent Posts

Minimum length for 3 non-adjacent G’s: G _ G _ G → 5 positions. Only o...
Positions: must satisfy $ g_2 \ge g_1 + 2 $, $ g_3 \ge g_2 + 2 $. The...
Only one such triplet of positions in 8? No — multiple.
But we already fixed C’s, and the 5 free positions are a subset of the...
So the 5 free positions may not even be contiguous.
Thus, placing 3 G’s in 5 arbitrary positions with no two adjacent depe...
Therefore, the number of ways to place 2 A’s and 3 G’s with no two A’s...
This makes direct counting messy.
Alternative approach: Use **recursive counting with states**, but for...
But let’s change direction: use **exponential generating functions wit...

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