Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
max {p6, p5, p2} = 5
⟨ ⁵ᵗʰa ⁴ᵗʰb ⟩, (ab)₁₀ ≤ 50
⟨ − ▧ − ▢ ▢ ▢ − ⟩, ▧ ≥ Σ▢
⟦2,4⟧ ∋ 1
⛔Avoid
⟨ ²ⁿᵈ↑ ⟩ after ⟨←⟩
0th → 4
⟦5,6⟧ ∋ 1,2,4
⟦2,5⟧ ∋ 0,3,4,6
----- Information -----
✅ 「max {p6, p5, p2} = 5」
The greatest element of { [6th], [5th], [2nd] } is 5.
There are 1440 permutations matching this pattern.
Examples: ⟨1340562⟩, ⟨5401326⟩, ⟨2513406⟩.
✅ 「⟨ ⁵ᵗʰa ⁴ᵗʰb ⟩, (ab)₁₀ ≤ 50」
(ab)₁₀ ∶= 10a + b.
There are 3720 permutations matching this pattern.
Examples: ⟨1325460⟩, ⟨5016432⟩, ⟨5362401⟩.
✅ 「⟨ − ▧ − ▢ ▢ ▢ − ⟩, ▧ ≥ Σ▢」
[5th] ≥ [3rd]+[2nd]+[1st].
There are 504 permutations matching this pattern.
Examples: ⟨2650314⟩, ⟨6531204⟩, ⟨4562103⟩.
✅ 「⟦2,4⟧ ∋ 1」
The closed interval given by 2 and 4 contains 1.
There are 1680 permutations matching this pattern.
Examples: ⟨0562314⟩, ⟨0521346⟩, ⟨6215430⟩.
⛔ 「⟨ ²ⁿᵈ↑ ⟩ after ⟨←⟩」
Given ⟨p6 p5 p4 p3 p2 p1 p0⟩, after “⟨←⟩” (left shift) it becomes ⟨p5 p4 p3 p2 p1 p0 p6⟩.
There are 2520 permutations avoiding this pattern.
Examples: ⟨5613402⟩, ⟨5431206⟩, ⟨0156324⟩.
⛔ 「0th → 4」
There are 4320 permutations avoiding this pattern.
Examples: ⟨2403156⟩, ⟨2406153⟩, ⟨3254106⟩.
⛔ 「⟦5,6⟧ ∋ 1,2,4」
The closed interval given by 5 and 6 contains 1, 2, 4.
There are 4536 permutations avoiding this pattern.
Examples: ⟨3256410⟩, ⟨3614502⟩, ⟨2453601⟩.
⛔ 「⟦2,5⟧ ∋ 0,3,4,6」
The closed interval given by 2 and 5 contains 0, 3, 4, 6.
There are 4704 permutations avoiding this pattern.
Examples: ⟨2405631⟩, ⟨2405613⟩, ⟨3612504⟩.
#125034_v2.9
2025-05-01 Q1(m=6)
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#125034_v2.9