2024-05-05 Q1(m=6)

2024-05-05 Q1(m=6)

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

⟨6th 5th 4th 3rd 2nd 1st 0th⟩

✅Match

⟨⋯ 3 ⋯ ? ⋯ 6 (?−3)⟩ (?≠6)

⟨⋯ 2 ⋯ 5 ⋯ 1 ⋯ 0 ⋯⟩

5th → a, 2nd → b, a+b=0+4n

⛔Avoid

⟨   ⁵ᵗʰ↑           ⟩ after ⟨→⟩

Jump(0,4) = 2

{p5, p4, p1} = ? + {0,1,2}

----- Information -----

🔲 「⟨⋯ 3 ⋯ ? ⋯ 6 (?−3)⟩ (?≠6)」

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

240 permutations match this pattern.

Examples: ⟨1340562⟩, ⟨3405261⟩, ⟨3520461⟩.

🔲 「⟨⋯ 2 ⋯ 5 ⋯ 1 ⋯ 0 ⋯⟩」

210 permutations match this pattern.

Examples: ⟨2543610⟩, ⟨2516340⟩, ⟨2356410⟩.

🔲 「5th → a, 2nd → b, a+b=0+4n」

[5th] + [2nd] = 0 | 4 | 8 | ⋯ .

960 permutations match this pattern.

Examples: ⟨2501346⟩, ⟨4120356⟩, ⟨0654213⟩.

🔳 「⟨   ⁵ᵗʰ↑           ⟩ after ⟨→⟩」

Given ⟨p6 p5 p4 p3 p2 p1 p0⟩, after “⟨→⟩” (right shift) it becomes ⟨p0 p6 p5 p4 p3 p2 p1⟩.

2520 permutations match this pattern.

Examples: ⟨1042563⟩, ⟨3241065⟩, ⟨4316025⟩.

🔳 「Jump(0,4) = 2」

There are 2 numbers between 0 and 4.

960 permutations match this pattern.

Examples: ⟨5016423⟩, ⟨0314625⟩, ⟨5214630⟩.

🔳 「{p5, p4, p1} = ? + {0,1,2}」

{ [5th], [4th], [1st] } = { ?, ?+1, ?+2 }.

720 permutations match this pattern.

Examples: ⟨0215634⟩, ⟨0641352⟩, ⟨6015423⟩.

#125034_v2.5

2024-05-05 Q1(m=6)

６５４３２１０

－－－－－－－

－－－－－６－

－－－－－６０

２－－－－６０

２－４－－６０

２－４５－６０

２－４５１６０

２３４５１６０

#125034_v2.5