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Home » Leopard Print or Cheetah Head? Why These Patterns Dominate Sight-Based Bataille! - Ready Digital AB

Leopard Print or Cheetah Head? Why These Patterns Dominate Sight-Based Bataille! - Ready Digital AB

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 Step 1: Place 3 non-adjacent A’s in 8 positions.

📌 To place 3 non-adjacent A’s in 8 positions, we use the combinatorial method of placing k non-adjacent items in n slots.

📌 This is equivalent to placing 3 A’s and 5 non-A’s, with at least one non-A between any two A’s.

📌 To count the number of ways to place 3 non-adjacent A’s in 8 positions:

📌 We use the stars and bars transformation: if we place 3 A’s with at least one non-A between them, we first reserve 2 non-A’s to enforce spacing. So, we place 3 A’s and use 2 of the 5 non-A’s as "separators" between them. That leaves $5 - 2 = 3$ non-A’s to distribute freely in the 4 possible gaps: before the first A, between A1 and A2, between A2 and A3, and after the third A.

📌 This is now equivalent to distributing 3 indistinct items (remaining non-A slots) into 4 distinct gaps (with no restriction), which has $ \binom{3 + 4 - 1}{3} = \binom{6}{3} = 20 $ ways.

📌 But since the non-A positions (the 5 positions not occupied by A) are fixed in sequence, and we are assigning specific labels (U, C, G) to them, we must instead use the method of placing A’s with spacing, then counting valid assignments.

📌 Alternative ( clearer) approach:

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