2024-03-15 Q1(m=6)

Rearrange the digits in ⟨1263045⟩ to meet the rules below.

⟨6th 5th 4th 3rd 2nd 1st 0th⟩

✅Match

3rd → 2

⟨? ⋯ 3 ⋯ (?+3) ⋯⟩ (?≠3,0)

⛔Avoid

⟨⋯ a ⋯ 0 ⋯⟩, a = 3|4|6

Sim⟨ ⁶ᵗʰ6 ⁵ᵗʰ3 ⁴ᵗʰ0 ³ʳᵈ1 ²ⁿᵈ4 ¹ˢᵗ5 ⁰ᵗʰ2 ⟩ = 0

max ⊢4⊣ ≥ 5

----- Information -----

🔲 「3rd → 2」

720 permutations match this pattern.

Examples: ⟨0362415⟩, ⟨3412650⟩, ⟨0562341⟩.

🔲 「⟨? ⋯ 3 ⋯ (?+3) ⋯⟩ (?≠3,0)」

?, 3, (?+3) are three different numbers.

720 permutations match this pattern.

Examples: ⟨2340615⟩, ⟨2305164⟩, ⟨2163540⟩.

🔳 「⟨⋯ a ⋯ 0 ⋯⟩, a = 3|4|6」

3780 permutations match this pattern.

Examples: ⟨3612054⟩, ⟨3026415⟩, ⟨3520146⟩.

🔳 「Sim⟨ ⁶ᵗʰ6 ⁵ᵗʰ3 ⁴ᵗʰ0 ³ʳᵈ1 ²ⁿᵈ4 ¹ˢᵗ5 ⁰ᵗʰ2 ⟩ = 0」

⟨pᵢ⟩ matches this pattern if and only if #{i: pᵢ = qᵢ} = 0, where ⟨qᵢ⟩ ∶= ⟨6301452⟩.

1854 permutations match this pattern.

Examples: ⟨3164025⟩, ⟨3510264⟩, ⟨3245106⟩.

🔳 「max ⊢4⊣ ≥ 5」

The greatest element of ⊢4⊣ is ≥ 5. Also written as B(x=4, r=1), ⊢4⊣ denotes the neighborhood of 4 with radius one.

2640 permutations match this pattern.

Examples: ⟨3105246⟩, ⟨6541203⟩, ⟨3256401⟩.

#125034_v2.4

2024-03-15 Q1(m=6)

６５４３２１０

－－－－－－－

－－－２－－－

１－－２－－－

１－－２－－４

１－－２－３４

１－０２－３４

１－０２６３４

１５０２６３４

#125034_v2.4