Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁴ᵗʰc ²ⁿᵈa ⁰ᵗʰb ⟩, a > b > c
⟨⋯ 1 ⋯ 5 ⋯ 4 ⋯ 0 ⋯⟩
⛔Avoid
⟨⋯ 2 ⋯ ? ⋯ 0 (?+1)⟩ (?≠0)
6th → 0|1|3|4|5
#125034_v2.10
Originating from a math proof, 125034 is a game driven by combinatorics, logic, and probability.
2025-10-31 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → a, 2nd → b, |a-b|=3
⟨ − ▧ − ▢ ▢ − ⟩, ▧ ≤ Σ▢
Jump(1,5) ≥ 2
⟨ ⁵ᵗʰa ⁴ᵗʰb ¹ˢᵗc ⟩, (abc)₁₀ ≥ 203
⟨⋯ a ⋯ 0 ⋯⟩, a = 2|3
⛔Avoid
⟨⋯ Perm(2,4) ⋯⟩
4th|3rd|1st|0th → 1
#125034_v2.10
2025-10-30 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁴ᵗʰa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 5
⟨⋯ 5 ⋯ ? ⋯ 4 (?−3)⟩ (?≠4)
4th → a, 2nd → b, a+b=3+5n
3rd → 1|2|3|5|6
max {p5, p2, p0} = 6
⛔Avoid
⟨⋯ 6 ⋯ 3 ⋯ 5 ⋯⟩
2nd → a, 0th → b, |a-b|=3
4th → a, 3rd → b, |a-b|=4
#125034_v2.10
2025-10-30 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
median {p5, p4, p0} = 4
5th → a, 4th → b, ab=5
⟨? ⋯ 2 ⋯ (?+2) ⋯⟩ (?≠2,0)
⛔Avoid
⟨⋯ Perm(2,5) ⋯⟩
#125034_v2.10
2025-10-28 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ ? ⋯ 1 ⋯ (?+1)⟩ (?≠1,0)
3rd → a, 1st → b, ab=2+5n
⟨⋯ Perm(0,2,3) ⋯⟩
⛔Avoid
max ⊢0⊣ ≤ 4
#125034_v2.10
2025-10-28 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 5 ⋯ ? 0 ⋯ (?−2)⟩ (?≠2)
⟨ ⁶ᵗʰa ³ʳᵈb ⟩, min⟦a,b⟧ = 0
⟨? ⋯ 1 (?−2) ⋯ 2 ⋯⟩ (?≠3)
⛔Avoid
6th|5th|3rd|1st|0th → 1
min ⊢4⊣ ≥ 3
5th → a, 2nd → b, |a-b|=5
#125034_v2.10
2025-10-26 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁶ᵗʰd ⁴ᵗʰc ³ʳᵈb ⁰ᵗʰa ⟩, a > b > c > d
1st → a, 0th → b, a+b=2+6n
2nd → 3
⛔Avoid
6th|3rd|1st|0th → 0
#125034_v2.10
2025-10-26 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
⟨Perm(0,1,5) Perm(2,3,4)⟩
⛔Avoid
max ⊢2⊣ ≤ 4
5th → a, 3rd → b, |a-b|=4
#125034_v2.10
2025-10-24 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
median {p5, p3, p1} = 2
max {p5, p2, p1} = 5
⟨⋯ ? ⋯ 4 ⋯ (?−1)⟩ (?≠4,5)
⛔Avoid
1 ∾ 2
⟨⋯ a ⋯ 4 ⋯⟩, a = 2|3|5
#125034_v2.10
2025-10-24 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
median {p2, p1, p0} = 2
⟨ ⁴ᵗʰa ³ʳᵈb ⁰ᵗʰc ⟩, a > b > c
⛔Avoid
⟨ ⁴ᵗʰ↑ ²ⁿᵈ↓ ⟩ after 2×⟨←⟩
⟨ − ▧ ▧ ▢ ▢ − ⟩, Σ▧ ≤ Σ▢
5th|3rd|1st|0th → 4
⟨⋯ ? ⋯ 2 ⋯ (?−3)⟩ (?≠5)
4th → a, 1st → b, a+b=1+4n
#125034_v2.10
2025-10-23 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? ⋯ 6 (?+2) ⋯ 0 ⋯⟩ (?≠4)
⟨⋯ 3 ⋯ ? 0 ⋯ (?−4)⟩ (?≠4)
4th|3rd|2nd → 0
5th → 4
#125034_v2.10
2025-10-23 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦1,3⟧ ∋ 2,5
1st → a, 0th → b, ab=4+5n
⛔Avoid
Sim⟨ ⁵ᵗʰ0 ⁴ᵗʰ2 ³ʳᵈ3 ²ⁿᵈ1 ¹ˢᵗ5 ⁰ᵗʰ4 ⟩ ≤ 1
⟨⋯ 2 ⋯ 5 ⋯⟩
#125034_v2.10
2025-10-21 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 3 ⋯ ? ⋯ 1 (?−2)⟩ (?≠3)
⛔Avoid
max {p5, p1, p0} = 5
5th → 0|1|2|3
⟨⋯ ? ⋯ 2 ⋯ (?−5)⟩
#125034_v2.10
2025-10-21 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd|1st → 0
4th → a, 1st → b, a+b=2+5n
⟨ ⁶ᵗʰa ⁵ᵗʰb ⟩, a > b
max {p3, p1, p0} = 5
⛔Avoid
⟨ ⁴ᵗʰa ²ⁿᵈb ⁰ᵗʰc ⟩, (abc)₁₀ ≤ 513
6th|5th|3rd|1st → 2
#125034_v2.10
2025-10-19 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(0,6) = 0
⟨⋯ a ⋯ 3 ⋯⟩, a = 0|1|2|4|5|6
{p6, p3, p1, p0} = ? + {0,1,2,3}
4th → 5
3rd → 1|2|5
⛔Avoid
⟨? ⋯ 6 ⋯ (?+3) ⋯⟩ (?≠3)
min ⊢5⊣ ≥ 2
#125034_v2.10
2025-10-19 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁴ᵗʰ↓ ⟩ after 2×⟨←⟩
⟨ ³ʳᵈ↓ ⟩ after ⟨→⟩
5th → a, 3rd → b, ab=0+5n
⛔Avoid
2nd → 0|1|3
5th|3rd|1st → 5
#125034_v2.10
2025-10-17 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → a, 4th → b, |a-b|=3
2nd → a, 0th → b, |a-b|=4
⟨ ⁵ᵗʰa ⁰ᵗʰb ⟩, (ab)₁₀ ≤ 40
⟨⋯ 3 ⋯ 0 ⋯ 6 ⋯ 2 ⋯⟩
⛔Avoid
5th → 0|1|6
⟨? ⋯ 3 ⋯ (?+4) ⋯⟩
⟨ − ▧ ▧ ▧ ▢ ▢ − ⟩, Σ▧ ≥ Σ▢
median {p6, p5, p2} = 5
#125034_v2.10
2025-10-17 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ³ʳᵈb ¹ˢᵗa ⁰ᵗʰc ⟩, a > b > c
{p5, p2, p1} = ? + {0,1,2}
⛔Avoid
5th → a, 2nd → b, ab=8
4th|3rd|2nd → 3
⟨ ³ʳᵈa ¹ˢᵗb ⟩, (ab)₁₀ ≥ 15
median {p4, p1, p0} = 2
#125034_v2.10
2025-10-16 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
{p3, p2, p1, p0} = ? + {0,1,2,3}
⟨ ⁶ᵗʰ↑ ⁵ᵗʰ↑ ⁴ᵗʰ= ³ʳᵈ↓ ²ⁿᵈ= ¹ˢᵗ↑ ⁰ᵗʰ↑ ⟩ after 6−⟨⇌⟩
⛔Avoid
⟦0,4⟧ ∋ 1,2,3
⟨? ⋯ 0 ⋯ (?+3) ⋯⟩ (?≠0)
#125034_v2.10
2025-10-16 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(2,3) = 2
Jump(3,4) ≥ 1
⟨ ▧ ▧ − − ▢ ▢ ⟩, Σ▧ = Σ▢
Jump(1,4) = 2
⛔Avoid
5th → a, 4th → b, a+b=2+4n
⟨ ⁵ᵗʰa ³ʳᵈb ⟩, min⟦a,b⟧ = 1
#125034_v2.10
2025-10-14 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? 1 ⋯ (?−2) ⋯ 3 ⋯⟩ (?≠3)
{p5, p1, p0} = ? + {0,1,2}
4th → a, 3rd → b, a+b=1
1st → a, 0th → b, a+b=1+4n
#125034_v2.10
2025-10-14 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁶ᵗʰa ²ⁿᵈb ⁰ᵗʰc ⟩, a > b > c
⟨ ⁴ᵗʰa ⁰ᵗʰb ⟩, min⟦a,b⟧ = 1
⛔Avoid
⟨⋯ 2 ⋯ a ⋯⟩, a = 0|1|3|5|6
2nd → a, 1st → b, a+b=3+6n
3rd → a, 2nd → b, a+b=1+6n
⟨ − ▧ ▧ ▧ − ▢ − ⟩, Σ▧ ≥ ▢
#125034_v2.10
2025-10-12 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(0,3) ≤ 2
⟨ ³ʳᵈa ¹ˢᵗb ⁰ᵗʰc ⟩, (abc)₁₀ ≥ 216
1st → 1|4|5|6
0th → 0|1|5
⟨ ⁶ᵗʰc ⁴ᵗʰa ⁰ᵗʰb ⟩, a > b > c
⛔Avoid
Jump(2,5) ≥ 2
min ⊢4⊣ ≤ 1
min ⊢2⊣ = 2
Jump(0,3) ≤ 1
#125034_v2.10
2025-10-12 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → a, 0th → b, a+b=7
Jump(2,4) ≤ 1
max ⊢0⊣ = 3
⛔Avoid
⟨ ³ʳᵈa ⁰ᵗʰb ⟩, min⟦a,b⟧ = 0
⟨ ⁴ᵗʰa ²ⁿᵈb ⟩, max⟦a,b⟧ = 5
#125034_v2.10
2025-10-10 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ ? ⋯ 3 ⋯ (?+3)⟩ (?≠3,0)
max ⊢1⊣ ≥ 5
⟨⋯ Perm(0,6) ⋯⟩
⟨? 4 ⋯ (?+4) ⋯ 0 ⋯⟩ (?≠0)
⟨ ⁴ᵗʰa ³ʳᵈb ²ⁿᵈc ⟩, (abc)₁₀ ≥ 540
#125034_v2.10
2025-10-10 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
min ⊢3⊣ ≤ 2
⟨ ⁵ᵗʰb ³ʳᵈa ⟩, a > b
min {p5, p2, p0} = 0
⟨⋯ Perm(0,1,4) ⋯⟩
⛔Avoid
3rd → a, 0th → b, a+b=3+5n
Sim⟨ ⁵ᵗʰ4 ⁴ᵗʰ3 ³ʳᵈ5 ²ⁿᵈ2 ¹ˢᵗ1 ⁰ᵗʰ0 ⟩ ≥ 1
⟨ − − ▧ ▧ − ▢ ⟩, Σ▧ ≤ ▢
4th → a, 0th → b, ab=5
{p4, p2, p1} = ? + {0,2,3}
max ⊢2⊣ ≤ 4
⟨⋯ 3 ⋯ 4 ⋯ 0 ⋯⟩
#125034_v2.10
2025-10-09 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁶ᵗʰa ¹ˢᵗb ⟩, (ab)₁₀ ≤ 10
0th → 0|1|6
⟨ ⁵ᵗʰa ²ⁿᵈb ⟩, min⟦a,b⟧ = 1
min ⊢3⊣ ≤ 1
5th → a, 1st → b, ab=12
⛔Avoid
⟨ ▧ ▧ − − − ▢ − ⟩, Σ▧ ≤ ▢
⟨ ³ʳᵈa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≤ 314
#125034_v2.10
2025-10-09 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(0,3) = 0
⟨ − ▧ − ▢ ▢ − ⟩, ▧ ≥ Σ▢
min ⊢5⊣ = 1
min ⊢2⊣ ≤ 1
⛔Avoid
3rd|2nd|1st → 1
3rd → 0|2|4|5
#125034_v2.10
2025-10-07 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁴ᵗʰa ³ʳᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≥ 234
⟨⋯ 3 ⋯ 2 ⋯⟩
1st → 3
2nd → 2|3|5
⛔Avoid
⟨ ³ʳᵈ↓ ⟩ after 2×⟨→⟩
#125034_v2.10
2025-10-07 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
6th → a, 3rd → b, a+b=8
max {p5, p3, p2} = 5
6th|5th|3rd|2nd|0th → 4
⟦0,5⟧ ∋ 1,2,3,4
⛔Avoid
⟦1,6⟧ ∋ 2,3,4,5
#125034_v2.10
2025-10-05 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(0,1) = 1
⟨ ⁶ᵗʰd ²ⁿᵈc ¹ˢᵗb ⁰ᵗʰa ⟩, a > b > c > d
⛔Avoid
5th → a, 2nd → b, |a-b|=2
3rd → 1|2|4|6
{p3, p2, p1} = ? + {0,1,2}
Sim⟨ ⁶ᵗʰ3 ⁵ᵗʰ4 ⁴ᵗʰ1 ³ʳᵈ0 ²ⁿᵈ2 ¹ˢᵗ5 ⁰ᵗʰ6 ⟩ ≥ 3
⟨ ⁶ᵗʰa ⁴ᵗʰb ⟩, a > b
#125034_v2.10
2025-10-05 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → a, 0th → b, |a-b|=5
3rd → a, 0th → b, a+b=2
5th → a, 2nd → b, a+b=6
⛔Avoid
1st → 3
#125034_v2.10
2025-10-03 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → a, 1st → b, ab=0
⟨? ⋯ 4 (?−4) ⋯ 0 ⋯⟩ (?≠4)
⟨ − − ▧ ▢ ▢ − − ⟩, ▧ ≥ Σ▢
3rd → 2|3|6
⟨ ⁵ᵗʰa ³ʳᵈb ⟩, (ab)₁₀ ≤ 42
#125034_v2.10
2025-10-03 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(1,2) ≥ 2
⟨⋯ 3 ⋯ ? 2 ⋯ (?−1)⟩ (?≠2,3)
⛔Avoid
⟨⋯ ? ⋯ 3 ⋯ (?+3)⟩ (?≠0)
#125034_v2.10
2025-10-02 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 0 ⋯ ? 6 ⋯ (?+3)⟩ (?≠3)
{p4, p3, p0} = ? + {0,1,3}
max ⊢3⊣ = 4
median {p3, p2, p1} = 2
⛔Avoid
median {p5, p4, p0} = 4
#125034_v2.10
2025-10-02 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
{p5, p4, p0} = ? + {0,1,2}
⟨ ▧ ▢ ▢ − − − ⟩, ▧ ≤ Σ▢
⟨ ⁵ᵗʰ↓ ⁴ᵗʰ↑ ³ʳᵈ↑ ²ⁿᵈ↓ ¹ˢᵗ↓ ⁰ᵗʰ↑ ⟩ after ⟨⇌⟩
{p3, p2, p0} = ? + {0,1,2}
#125034_v2.10
Subscribe to:
Comments (Atom)