2024-03-11 Q1(m=6)

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

⟨6th 5th 4th 3rd 2nd 1st 0th⟩

✅Match

⟦5,6⟧ ∋ 0,1,2,4

⟨ ⁶ᵗʰa ⁵ᵗʰb     ²ⁿᵈc ¹ˢᵗd   ⟩, a > b > c > d

min ⊢5⊣ ≤ 1

Jump(1,2) = 1

⛔Avoid

2nd → 2

⟨? ⋯ 4 ⋯ (?−3) ⋯⟩ (?≠4)

----- Information -----

🔲 「⟦5,6⟧ ∋ 0,1,2,4」

The closed interval given by 5 and 6 contains 0, 1, 2, 4.

336 permutations match this pattern.

Examples: ⟨5231046⟩, ⟨6213405⟩, ⟨6213045⟩.

🔲 「⟨ ⁶ᵗʰa ⁵ᵗʰb     ²ⁿᵈc ¹ˢᵗd   ⟩, a > b > c > d」

210 permutations match this pattern.

Examples: ⟨6501432⟩, ⟨6502431⟩, ⟨6503421⟩.

🔲 「min ⊢5⊣ ≤ 1」

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

2640 permutations match this pattern.

Examples: ⟨4023615⟩, ⟨0651432⟩, ⟨6134052⟩.

🔲 「Jump(1,2) = 1」

There is 1 number between 1 and 2.

1200 permutations match this pattern.

Examples: ⟨4560231⟩, ⟨1326405⟩, ⟨5314206⟩.

🔳 「2nd → 2」

720 permutations match this pattern.

Examples: ⟨4561230⟩, ⟨6451203⟩, ⟨3104265⟩.

🔳 「⟨? ⋯ 4 ⋯ (?−3) ⋯⟩ (?≠4)」

?, 4, (?−3) are three different numbers.

1080 permutations match this pattern.

Examples: ⟨3461025⟩, ⟨5143602⟩, ⟨3216540⟩.

#125034_v2.4

2024-03-11 Q1(m=6)

６５４３２１０

－－－－－－－

６－－－－－－

６－－－－－５

６３－－－－５

６３－－１－５

６３－－１０５

６３２－１０５

６３２４１０５

#125034_v2.4