2025-08-31 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
median {p6, p2, p0} = 2
⟨ − − ▧ ▧ ▢ ▢ ▢ ⟩, Σ▧ ≤ Σ▢
⟨? 3 ⋯ (?+3) ⋯ 2 ⋯⟩ (?≠3,0)
Sim⟨ ⁶ᵗʰ1 ⁵ᵗʰ2 ⁴ᵗʰ4 ³ʳᵈ5 ²ⁿᵈ3 ¹ˢᵗ6 ⁰ᵗʰ0 ⟩ ≥ 2
⛔Avoid
⟨ ⁵ᵗʰa ²ⁿᵈb ⟩, max⟦a,b⟧ = 5
4th → a, 3rd → b, a+b=0+4n
#125034_v2.10
2025-08-29 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰa ³ʳᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≥ 530
Sim⟨ ⁶ᵗʰ1 ⁵ᵗʰ6 ⁴ᵗʰ3 ³ʳᵈ4 ²ⁿᵈ0 ¹ˢᵗ5 ⁰ᵗʰ2 ⟩ = 3
⛔Avoid
Sim⟨ ⁶ᵗʰ1 ⁵ᵗʰ5 ⁴ᵗʰ4 ³ʳᵈ3 ²ⁿᵈ6 ¹ˢᵗ2 ⁰ᵗʰ0 ⟩ = 0
⟨ − ▧ ▧ − − ▢ ▢ ⟩, Σ▧ ≥ Σ▢
⟨ ▧ ▧ − − − ▢ ▢ ⟩, Σ▧ ≤ Σ▢
#125034_v2.10
2025-08-29 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → 0|2|3
⟨⋯ Perm(1,2) ⋯⟩
⟨ − ▧ ▧ ▢ ▢ ▢ ⟩, Σ▧ ≥ Σ▢
min ⊢4⊣ = 2
⛔Avoid
5th → a, 4th → b, |a-b|=1
⟨ ³ʳᵈb ²ⁿᵈa ⁰ᵗʰc ⟩, a > b > c
#125034_v2.10
2025-08-28 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰa ²ⁿᵈb ⟩, min⟦a,b⟧ = 0
6th|4th|3rd|2nd|0th → 5
⟨⋯ 2 ⋯ ? 6 ⋯ (?+2)⟩ (?≠4)
⟦3,6⟧ ∋ 4,5
⛔Avoid
⟨ ⁵ᵗʰa ³ʳᵈb ⁰ᵗʰc ⟩, (abc)₁₀ ≤ 132
#125034_v2.10
2025-08-28 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
Sim⟨ ⁵ᵗʰ0 ⁴ᵗʰ5 ³ʳᵈ1 ²ⁿᵈ2 ¹ˢᵗ3 ⁰ᵗʰ4 ⟩ ≤ 1
⟨⋯ a ⋯ 2 ⋯⟩, a = 1|4|5
⛔Avoid
⟨? ⋯ 4 ⋯ (?−1) ⋯⟩ (?≠4,5)
⟦3,4⟧ ∋ 2
max {p5, p2, p1} = 4
3rd|2nd|1st|0th → 1
⟨ ³ʳᵈa ¹ˢᵗb ⟩, (ab)₁₀ ≥ 05
5th → a, 3rd → b, |a-b|=5
⟨ ⁵ᵗʰc ⁴ᵗʰb ¹ˢᵗa ⟩, a > b > c
#125034_v2.10
2025-08-26 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ a ⋯ 1 ⋯⟩, a = 2|5
⟨ ⁴ᵗʰa ³ʳᵈb ⁰ᵗʰc ⟩, (abc)₁₀ ≥ 123
⟨ − ▧ ▧ ▢ ▢ − ⟩, Σ▧ ≤ Σ▢
⛔Avoid
⟨ ⁴ᵗʰa ¹ˢᵗb ⟩, (ab)₁₀ ≥ 14
⟨ − ▧ ▧ ▢ − − ⟩, Σ▧ ≤ ▢
⟨⋯ 2 ⋯ 3 ⋯⟩
#125034_v2.10
2025-08-26 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
6th → a, 1st → b, ab=15
⟨⋯ 0 ⋯ 6 ⋯ 1 ⋯ 3 ⋯⟩
⟨⋯ 0 ⋯ a ⋯⟩, a = 2|5
⛔Avoid
0 ∾ 2
Sim⟨ ⁶ᵗʰ5 ⁵ᵗʰ4 ⁴ᵗʰ3 ³ʳᵈ0 ²ⁿᵈ1 ¹ˢᵗ2 ⁰ᵗʰ6 ⟩ ≤ 1
#125034_v2.10
2025-08-24 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁶ᵗʰa ⁵ᵗʰb ⁰ᵗʰc ⟩, (abc)₁₀ ≤ 125
⟨⋯ 1 ⋯ 6 ⋯ 2 ⋯ 3 ⋯⟩
⟨ ⁶ᵗʰ↑ ⁵ᵗʰ= ⁴ᵗʰ↓ ³ʳᵈ↑ ²ⁿᵈ↓ ¹ˢᵗ= ⁰ᵗʰ↑ ⟩ after 6−⟨⇌⟩
⛔Avoid
5th|4th|3rd|0th → 5
0th → 1|2|4|6
#125034_v2.10
2025-08-24 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 4 ⋯ 3 ⋯⟩
⟨⋯ 4 ⋯ ? 0 ⋯ (?−1)⟩ (?≠1)
⟨ ▧ − − − ▢ ▢ ⟩, ▧ ≤ Σ▢
⛔Avoid
3 ∾ 4 ∾ 5
⟨ ⁰ᵗʰ↓ ⟩ after ⟨→⟩
⟨ ▧ ▧ − − ▢ ▢ ⟩, Σ▧ ≤ Σ▢
median {p4, p3, p1} = 2
#125034_v2.10
2025-08-22 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦5,6⟧ ∋ 2,4
6th|4th|2nd → 5
2nd → 0|1|2|4|5
6th → a, 2nd → b, ab=2+4n
⟨ ⁴ᵗʰb ³ʳᵈa ⁰ᵗʰc ⟩, a > b > c
⛔Avoid
⟨? ⋯ 4 ⋯ (?−4) ⋯⟩ (?≠4)
⟦2,3⟧ ∋ 4,5
median {p5, p1, p0} = 1
#125034_v2.10
2025-08-22 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? 3 ⋯ (?−3) ⋯ 5 ⋯⟩ (?≠3)
⟨ ⁵ᵗʰb ⁴ᵗʰc ²ⁿᵈa ⟩, a > b > c
⛔Avoid
⟦0,1⟧ ∋ 2,5
#125034_v2.10
2025-08-21 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰa ²ⁿᵈb ⟩, min⟦a,b⟧ = 2
⟦0,3⟧ ∋ 1,2,5
⛔Avoid
min ⊢6⊣ = 2
⟨ ⁶ᵗʰa ⁵ᵗʰb ⁰ᵗʰc ⟩, (abc)₁₀ ≤ 240
⟦0,5⟧ ∋ 6
min ⊢5⊣ ≤ 3
#125034_v2.10
2025-08-21 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ ? ⋯ 0 ⋯ (?+2)⟩ (?≠0)
⟨ ⁵ᵗʰa ⁰ᵗʰb ⟩, (ab)₁₀ ≤ 23
⟨⋯ Perm(1,2,5) ⋯⟩
⛔Avoid
⟨⋯ ? ⋯ 0 ⋯ (?−1)⟩ (?≠1)
2 ∾ 3 ∾ 4
5th → a, 0th → b, ab=6
#125034_v2.10
2025-08-19 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(2,3) = 1
median {p5, p3, p0} = 3
4th → 0|2|4
⛔Avoid
Jump(0,2) = 0
median {p4, p3, p1} = 2
⟨⋯ 1 ⋯ 3 ⋯⟩
⟨⋯ 2 ⋯ ? 3 ⋯ (?+1)⟩ (?≠3,2)
#125034_v2.10
2025-08-19 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ▧ ▧ − − ▢ − − ⟩, Σ▧ ≤ ▢
2nd → a, 1st → b, a+b=9
6th|5th|3rd|2nd|0th → 3
⟨? ⋯ 3 (?+1) ⋯ 6 ⋯⟩ (?≠3,2)
⟨ ²ⁿᵈ↑ ⟩ after ⟨←⟩
⛔Avoid
⟨⋯ 3 ⋯ 2 ⋯ 0 ⋯⟩
min {p5, p3, p2} = 2
#125034_v2.10
2025-08-17 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 4 ⋯ ? 5 ⋯ (?−1)⟩ (?≠5,6)
⟨ ⁶ᵗʰ↑ ²ⁿᵈ↑ ⟩ after 3×⟨→⟩
⛔Avoid
⟨⋯ 0 ⋯ 5 ⋯⟩
3rd → 0|1|2|3|4
⟨ ⁵ᵗʰa ³ʳᵈb ²ⁿᵈc ¹ˢᵗd ⟩, a > b > c > d
⟨ ▧ ▧ − − − ▢ − ⟩, Σ▧ ≤ ▢
#125034_v2.10
2025-08-17 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
2nd → a, 0th → b, |a-b|=1
⟨? 1 ⋯ (?−3) ⋯ 2 ⋯⟩ (?≠4)
⟨ ⁵ᵗʰ↓ ⁴ᵗʰ↑ ³ʳᵈ↑ ²ⁿᵈ↑ ¹ˢᵗ↓ ⁰ᵗʰ↓ ⟩ after 5−⟨⋯⟩
#125034_v2.10
2025-08-15 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰa ³ʳᵈb ⟩, max⟦a,b⟧ = 6
⟨ ⁶ᵗʰa ⁵ᵗʰb ⟩, a > b
⟦1,5⟧ ∋ 3,4,6
⟨⋯ ? ⋯ 5 ⋯ (?−4)⟩ (?≠5)
⛔Avoid
⟨ ³ʳᵈa ⁰ᵗʰb ⟩, (ab)₁₀ ≥ 53
⟦3,5⟧ ∋ 4
⟦0,6⟧ ∋ 3
#125034_v2.10
2025-08-15 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
2nd → a, 0th → b, ab=12
4th → a, 3rd → b, |a-b|=3
⟦0,4⟧ ∋ 5
⛔Avoid
4th → a, 2nd → b, a+b=0+4n
2nd → 1|2|4
#125034_v2.10
2025-08-14 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
6th → 0
⟨ ⁶ᵗʰ↑ ⁵ᵗʰ↓ ⁴ᵗʰ= ³ʳᵈ↑ ²ⁿᵈ= ¹ˢᵗ↓ ⁰ᵗʰ↑ ⟩ after 6−⟨⇌⟩
⛔Avoid
⟨ ³ʳᵈa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≥ 124
#125034_v2.10
2025-08-14 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 4 ⋯ ? ⋯ 5 (?−3)⟩ (?≠5)
⟨? 3 ⋯ (?−3) ⋯ 2 ⋯⟩ (?≠3)
#125034_v2.10
2025-08-12 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
median {p5, p4, p3} = 3
4th → a, 2nd → b, |a-b|=3
0 ∾ 1 ∾ 2 ∾ 3 ∾ 5 ∾ 6
⟨ ⁵ᵗʰa ¹ˢᵗb ⟩, min⟦a,b⟧ = 1
⛔Avoid
⟨ ⁶ᵗʰa ²ⁿᵈb ⟩, max⟦a,b⟧ = 6
#125034_v2.10
2025-08-12 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? ⋯ 5 (?+1) ⋯ 0 ⋯⟩ (?≠4)
⛔Avoid
⟨ ⁵ᵗʰa ²ⁿᵈb ⁰ᵗʰc ⟩, a > b > c
⟨⋯ a ⋯ 5 ⋯⟩, a = 0|1|2|4
⟦1,4⟧ ∋ 0
----- Information -----
✅ 「⟨? ⋯ 5 (?+1) ⋯ 0 ⋯⟩ (?≠4)」
• ?, 5, (?+1) are distinct digits.
• ? is at the 5th (leftmost) position.
• 5 and (?+1) are adjacent.
There are 36 permutations matching this pattern.
Examples: ⟨152034⟩, ⟨145203⟩, ⟨152340⟩.
⛔ 「⟨ ⁵ᵗʰa ²ⁿᵈb ⁰ᵗʰc ⟩, a > b > c」
There are 600 permutations avoiding this pattern.
Examples: ⟨502143⟩, ⟨104352⟩, ⟨314502⟩.
⛔ 「⟨⋯ a ⋯ 5 ⋯⟩, a = 0|1|2|4」
At least one of {0,1,2,4} is to the left of 5.
There are 144 permutations avoiding this pattern.
Examples: ⟨521340⟩, ⟨543120⟩, ⟨514023⟩.
⛔ 「⟦1,4⟧ ∋ 0」
Digit 0 is positioned between digits 1 and 4.
There are 480 permutations avoiding this pattern.
Examples: ⟨514302⟩, ⟨154302⟩, ⟨204531⟩.
#125034_v2.10
2025-08-10 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 2 ⋯ 5 ⋯ 3 ⋯ 6 ⋯⟩
4th → a, 2nd → b, ab=24
⛔Avoid
max ⊢0⊣ ≥ 3
#125034_v2.9
2025-08-10 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰ↑ ²ⁿᵈ↓ ⟩ after ⟨←⟩
⟨⋯ ? ⋯ 2 ⋯ (?−1)⟩ (?≠2,3)
⟨⋯ 3 ⋯ 4 ⋯⟩
⛔Avoid
2nd → 4|5
⟨? ⋯ 3 ⋯ (?+1) ⋯⟩ (?≠3,2)
⟨ − ▧ ▢ ▢ − − ⟩, ▧ ≥ Σ▢
#125034_v2.9
2025-08-08 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨Perm(0,1,2,5) Perm(3,4,6)⟩
{p6, p5, p2, p0} = ? + {0,1,2,3}
⟨ ⁶ᵗʰa ⁵ᵗʰb ⁰ᵗʰc ⟩, (abc)₁₀ ≤ 210
⟨ ▧ ▧ ▧ − ▢ − − ⟩, Σ▧ = ▢
#125034_v2.9
2025-08-08 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
0 ∾ 2 ∾ 3 ∾ 4 ∾ 5
{p5, p2, p0} = ? + {0,1,2}
⛔Avoid
⟨ ▧ ▧ ▢ ▢ ▢ − ⟩, Σ▧ ≤ Σ▢
min {p5, p3, p2} = 1
{p5, p2, p1} = ? + {0,2,3}
#125034_v2.9
2025-08-07 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦1,3⟧ ∋ 4
Jump(3,6) = 2
2nd → a, 0th → b, |a-b|=3
⟨? ⋯ 6 ⋯ (?−1) ⋯⟩ (?≠6)
⛔Avoid
min {p6, p4, p0} = 1
⟨⋯ 4 ⋯ a ⋯⟩, a = 0|1|2
#125034_v2.9
2025-08-07 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
median {p5, p1, p0} = 3
⟨ − ▧ ▢ ▢ ▢ − ⟩, ▧ ≥ Σ▢
⛔Avoid
⟨⋯ 1 ⋯ 2 ⋯⟩
⟨⋯ Perm(1,3) ⋯⟩
5th|4th|3rd|0th → 2
2nd → a, 0th → b, a+b=1+5n
#125034_v2.9
2025-08-05 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
1st → a, 0th → b, |a-b|=1
⟨ ⁴ᵗʰa ³ʳᵈb ⁰ᵗʰc ⟩, (abc)₁₀ ≥ 153
⟦0,2⟧ ∋ 3,4
⛔Avoid
⟨ ⁵ᵗʰ↑ ⁴ᵗʰ↓ ⟩ after 3×⟨→⟩
{p4, p2, p0} = ? + {0,1,2}
2nd → 0|4
#125034_v2.9
2025-08-05 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
min {p5, p4, p0} = 2
{p6, p5, p1, p0} = ? + {0,2,3,4}
⛔Avoid
3rd → a, 0th → b, |a-b|=3
⟨⋯ 0 ⋯ a ⋯⟩, a = 1|2|6
⟨⋯ 2 ⋯ 5 ⋯⟩
#125034_v2.9
2025-08-03 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → a, 2nd → b, ab=0
min {p6, p5} = 1
⟦0,6⟧ ∋ 1,3
⛔Avoid
⟨⋯ 0 ⋯ 5 ⋯⟩
min ⊢4⊣ ≤ 1
6th|5th|4th → 5
#125034_v2.9
2025-08-03 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(0,5) = 1
⟨? ⋯ 1 (?−3) ⋯ 4 ⋯⟩ (?≠4)
min {p4, p2, p0} = 1
⛔Avoid
⟨ ⁴ᵗʰa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≤ 243
#125034_v2.9
2025-08-01 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Sim⟨ ⁶ᵗʰ5 ⁵ᵗʰ3 ⁴ᵗʰ4 ³ʳᵈ1 ²ⁿᵈ0 ¹ˢᵗ6 ⁰ᵗʰ2 ⟩ = 3
max ⊢2⊣ = 2
min ⊢6⊣ = 3
6th → a, 5th → b, |a-b|=3
⛔Avoid
⟦2,3⟧ ∋ 0,1
min {p5, p4, p1} = 0
#125034_v2.9
2025-08-01 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰb ²ⁿᵈa ⟩, a > b
1st → 0|2|5
min {p4, p3, p1} = 0
⛔Avoid
⟨⋯ 5 ⋯ a ⋯⟩, a = 1|3|4
⟨? 1 ⋯ (?+1) ⋯ 5 ⋯⟩ (?≠1,0)
4th → a, 1st → b, a+b=0+5n
⟨ ³ʳᵈc ²ⁿᵈb ⁰ᵗʰa ⟩, a > b > c
⟨? ⋯ 2 (?+3) ⋯ 3 ⋯⟩ (?≠2)
⟨ ⁴ᵗʰa ¹ˢᵗb ⁰ᵗʰc ⟩, (abc)₁₀ ≥ 235
#125034_v2.9
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