2023-11-30 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨5th 4th 3rd 2nd 1st 0th⟩

✅Match

Sim⟨ ⁵ᵗʰ3 ⁴ᵗʰ4 ³ʳᵈ0 ²ⁿᵈ1 ¹ˢᵗ5 ⁰ᵗʰ2 ⟩ ≥ 2

⟨⋯ Perm(0,2) ⋯⟩

⟨⋯ a ⋯ 3 ⋯⟩, a = 0|1|4|5

⟨⋯ 4 ⋯ 0 ⋯⟩

⟨ ⁵ᵗʰa       ¹ˢᵗc ⁰ᵗʰb ⟩, a > b > c

⛔Avoid

5th|3rd|0th → 2

----- Information -----

🔲 「Sim⟨ ⁵ᵗʰ3 ⁴ᵗʰ4 ³ʳᵈ0 ²ⁿᵈ1 ¹ˢᵗ5 ⁰ᵗʰ2 ⟩ ≥ 2」

⟨pᵢ⟩ matches this pattern if and only if #{i: pᵢ = qᵢ} ≥ 2, where ⟨qᵢ⟩ ∶= ⟨340152⟩.

191 permutations match this pattern.

Examples: ⟨150342⟩, ⟨345021⟩, ⟨530124⟩.

🔲 「⟨⋯ Perm(0,2) ⋯⟩」

0,2 are adjacent.

240 permutations match this pattern.

Examples: ⟨302451⟩, ⟨102435⟩, ⟨420531⟩.

🔲 「⟨⋯ a ⋯ 3 ⋯⟩, a = 0|1|4|5」

576 permutations match this pattern.

Examples: ⟨045213⟩, ⟨451302⟩, ⟨023541⟩.

🔲 「⟨⋯ 4 ⋯ 0 ⋯⟩」

360 permutations match this pattern.

Examples: ⟨415230⟩, ⟨143025⟩, ⟨231540⟩.

🔲 「⟨ ⁵ᵗʰa       ¹ˢᵗc ⁰ᵗʰb ⟩, a > b > c」

120 permutations match this pattern.

Examples: ⟨352401⟩, ⟨521403⟩, ⟨530412⟩.

🔳 「5th|3rd|0th → 2」

360 permutations match this pattern.

Examples: ⟨531402⟩, ⟨145032⟩, ⟨510342⟩.

#125034_v2.2

2023-11-30 WR

🔲🔲🔲🔲✅🔲

🔲🔲✅🔲✅🔲

🔲🔲✅🔲✅✅

🔲✅✅🔲✅✅

🔲✅✅✅✅✅

✅✅✅✅✅✅

#125034_v2.2