Originating from a math proof, 125034 is a game driven by combinatorics, logic, and probability.
2025-03-30 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → a, 1st → b, a+b=2+4n
6th → 1
5th → 6
{p5, p1, p0} = ? + {0,2,4}
4th → a, 2nd → b, a+b=3+5n
⛔Avoid
4th → a, 1st → b, |a-b|=1
#125034_v2.8
2025-03-28 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ Perm(4,6) ⋯⟩
⟨ ⁶ᵗʰa ³ʳᵈb ⟩, min⟦a,b⟧ = 2
median {p3, p2, p1} = 1
⟨⋯ Perm(1,2,3) ⋯⟩
⛔Avoid
⟨? 6 ⋯ (?−2) ⋯ 2 ⋯⟩ (?≠6)
max ⊢1⊣ = 3
#125034_v2.8
2025-03-28 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ Perm(0,4,5) ⋯⟩
3rd → a, 2nd → b, |a-b|=5
⟨ ³ʳᵈa ²ⁿᵈb ⟩, a > b
5th → 2|3|5
⛔Avoid
4th → 0|1|4
median {p5, p3, p2} = 3
#125034_v2.8
2025-03-27 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 6 ⋯ 4 ⋯ 0 ⋯⟩
⟨⋯ 5 ⋯ 1 ⋯ 6 ⋯⟩
5th → 3|5|6
Jump(2,4) = 1
⛔Avoid
⟦2,3⟧ ∋ 1,4,5,6
min ⊢2⊣ = 1
#125034_v2.8
2025-03-27 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
min {p2, p1} = 2
Sim⟨ ⁵ᵗʰ0 ⁴ᵗʰ1 ³ʳᵈ4 ²ⁿᵈ3 ¹ˢᵗ5 ⁰ᵗʰ2 ⟩ ≥ 2
1st → 0|1|3|4
5th → a, 4th → b, |a-b|=1
⛔Avoid
⟨⋯ 1 ⋯ 5 ⋯ 4 ⋯⟩
1st → 4
#125034_v2.8
2025-03-25 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 4 ⋯ a ⋯⟩, a = 0|3|5
⟨ ⁶ᵗʰa ³ʳᵈc ²ⁿᵈd ⁰ᵗʰb ⟩, a > b > c > d
⟨ ⁴ᵗʰa ⁰ᵗʰb ⟩, min⟦a,b⟧ = 1
⟨ ⁶ᵗʰ↓ ⁴ᵗʰ↓ ¹ˢᵗ↓ ⟩ after 2×⟨→⟩
#125034_v2.8
2025-03-25 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ Perm(0,2,4) ⋯⟩
5th → a, 2nd → b, |a-b|=1
⟨ ⁵ᵗʰa ²ⁿᵈb ⟩, min⟦a,b⟧ = 0
⛔Avoid
⟨⋯ Perm(0,3) ⋯⟩
{p4, p2, p1} = ? + {0,2,3}
Jump(1,2) ≥ 2
5th|2nd|0th → 0
max ⊢3⊣ = 3
#125034_v2.8
2025-03-23 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=4+5n
⟨ ⁶ᵗʰa ²ⁿᵈb ⟩, max⟦a,b⟧ = 5
{p5, p3, p2, p1} = ? + {0,1,2,4}
⟨ ⁶ᵗʰ↑ ⁰ᵗʰ↓ ⟩ after ⟨←⟩
5th → a, 4th → b, |a-b|=3
#125034_v2.8
2025-03-23 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ³ʳᵈa ²ⁿᵈb ⁰ᵗʰc ⟩, (abc)₁₀ ≥ 310
5th → a, 1st → b, a+b=4
min ⊢3⊣ = 2
⛔Avoid
⟨ ³ʳᵈa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 5
⟨⋯ Perm(0,1) ⋯⟩
#125034_v2.8
2025-03-21 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
min ⊢4⊣ = 3
⟨ ⁵ᵗʰa ⁴ᵗʰc ²ⁿᵈb ⟩, a > b > c
5th → a, 3rd → b, ab=30
max ⊢0⊣ ≥ 4
6th → a, 1st → b, |a-b|=2
⟨⋯ 3 ⋯ a ⋯⟩, a = 0|4|5
⛔Avoid
⟨ ⁴ᵗʰa ²ⁿᵈb ⟩, max⟦a,b⟧ = 5
#125034_v2.8
2025-03-21 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
1st → a, 0th → b, a+b=5
⟦3,5⟧ ∋ 1,2
min {p5, p4, p1} = 1
⛔Avoid
⟨ ⁴ᵗʰa ²ⁿᵈb ⟩, min⟦a,b⟧ = 0
median {p5, p3, p0} = 3
#125034_v2.8
2025-03-20 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} = 1
⟨⋯ 1 ⋯ ? ⋯ 0 (?+1)⟩ (?≠0)
⟨ ³ʳᵈa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 5
min ⊢6⊣ ≥ 2
5th → 0|1|4
#125034_v2.8
2025-03-20 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → a, 2nd → b, |a-b|=1
⟦2,5⟧ ∋ 0,3
⟨⋯ 0 ⋯ ? 1 ⋯ (?−2)⟩ (?≠3)
⛔Avoid
⟨ ⁵ᵗʰ↓ ⁴ᵗʰ↑ ³ʳᵈ↑ ²ⁿᵈ↑ ¹ˢᵗ↑ ⁰ᵗʰ↓ ⟩ after 5−⟨⇌⟩
#125034_v2.8
2025-03-18 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 3 ⋯ 4 ⋯ 5 ⋯⟩
max ⊢0⊣ ≤ 4
3rd → a, 0th → b, ab=0+4n
⛔Avoid
⟨⋯ ? ⋯ 1 ⋯ (?−1)⟩ (?≠1,2)
Sim⟨ ⁵ᵗʰ3 ⁴ᵗʰ5 ³ʳᵈ1 ²ⁿᵈ0 ¹ˢᵗ4 ⁰ᵗʰ2 ⟩ ≤ 1
5th → a, 1st → b, |a-b|=1
#125034_v2.8
2025-03-18 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁶ᵗʰd ³ʳᵈb ²ⁿᵈa ¹ˢᵗc ⟩, a > b > c > d
min ⊢6⊣ = 2
⟨⋯ Perm(3,4,6) ⋯⟩
⟨⋯ ? ⋯ 3 ⋯ (?−4)⟩
⛔Avoid
⟨ ⁶ᵗʰ↑ ⁵ᵗʰ↓ ⁴ᵗʰ↑ ³ʳᵈ= ²ⁿᵈ↓ ¹ˢᵗ↑ ⁰ᵗʰ↓ ⟩ after ⟨⇌⟩
#125034_v2.8
2025-03-16 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁶ᵗʰa ⁴ᵗʰb ⁰ᵗʰc ⟩, (abc)₁₀ ≤ 540
min ⊢3⊣ = 1
Jump(0,4) = 4
⟨⋯ 6 ⋯ 2 ⋯ 4 ⋯⟩
⛔Avoid
6th|5th|3rd|2nd|1st → 4
#125034_v2.8
2025-03-16 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
4th → 0|1|4
{p5, p2, p0} = ? + {0,2,3}
⟨⋯ Perm(0,3) ⋯⟩
5th → a, 0th → b, a+b=1+5n
⛔Avoid
⟨ ⁵ᵗʰ↓ ⁴ᵗʰ↑ ³ʳᵈ↓ ²ⁿᵈ↓ ¹ˢᵗ↑ ⁰ᵗʰ↑ ⟩ after 5−⟨⋯⟩
#125034_v2.8
2025-03-14 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(4,5) ≤ 1
⟨⋯ Perm(1,3,4) ⋯⟩
5th|3rd → 3
⟨ ³ʳᵈa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 4
⛔Avoid
⟨ ⁶ᵗʰa ⁰ᵗʰb ⟩, (ab)₁₀ ≥ 10
#125034_v2.8
2025-03-14 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
4th → 1|2|3
Sim⟨ ⁵ᵗʰ0 ⁴ᵗʰ3 ³ʳᵈ4 ²ⁿᵈ1 ¹ˢᵗ2 ⁰ᵗʰ5 ⟩ = 0
5th → a, 2nd → b, |a-b|=5
⛔Avoid
Jump(1,5) ≤ 3
#125034_v2.8
2025-03-13 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
0th → 1|3|5|6
⟨ ²ⁿᵈb ⁰ᵗʰa ⟩, a > b
Sim⟨ ⁶ᵗʰ5 ⁵ᵗʰ1 ⁴ᵗʰ6 ³ʳᵈ0 ²ⁿᵈ4 ¹ˢᵗ3 ⁰ᵗʰ2 ⟩ = 0
⟨ ⁴ᵗʰa ³ʳᵈb ²ⁿᵈc ⟩, (abc)₁₀ ≥ 460
⛔Avoid
max ⊢2⊣ ≤ 4
⟨⋯ a ⋯ 3 ⋯⟩, a = 0|4|5
max ⊢4⊣ ≤ 5
min ⊢2⊣ ≤ 1
#125034_v2.8
2025-03-13 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? ⋯ 0 (?+1) ⋯ 4 ⋯⟩ (?≠0)
⟨ ⁵ᵗʰa ²ⁿᵈb ⟩, max⟦a,b⟧ = 4
3rd → a, 0th → b, |a-b|=1
⛔Avoid
⟦3,5⟧ ∋ 2
#125034_v2.8
2025-03-11 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(0,4) ≥ 2
5th → 2|5
⛔Avoid
{p5, p3, p2} = ? + {0,2,3}
⟨ ⁵ᵗʰa ³ʳᵈb ⟩, max⟦a,b⟧ = 4
⟨ ⁵ᵗʰa ³ʳᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≥ 435
⟨⋯ 2 ⋯ 0 ⋯ 1 ⋯⟩
median {p2, p1, p0} = 1
#125034_v2.8
2025-03-11 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦0,6⟧ ∋ 1,2,3,4
Jump(2,5) = 4
⟨ ⁶ᵗʰa ⁴ᵗʰc ²ⁿᵈd ⁰ᵗʰb ⟩, a > b > c > d
⛔Avoid
4th → 1|2|4
#125034_v2.8
2025-03-09 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(3,6) = 4
⟨ ⁶ᵗʰb ¹ˢᵗa ⁰ᵗʰc ⟩, a > b > c
⟨ ⁵ᵗʰc ³ʳᵈd ²ⁿᵈa ⁰ᵗʰb ⟩, a > b > c > d
⛔Avoid
{p6, p5, p4, p0} = ? + {0,1,2,4}
#125034_v2.8
2025-03-09 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ Perm(0,1,5) ⋯⟩
⟨ ⁵ᵗʰ↓ ⁴ᵗʰ↓ ³ʳᵈ↑ ²ⁿᵈ↓ ¹ˢᵗ↑ ⁰ᵗʰ↑ ⟩ after 5−⟨⋯⟩
⟨⋯ ? ⋯ 3 ⋯ (?−4)⟩
#125034_v2.8
2025-03-07 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
6th → 3|4
⟨⋯ 1 ⋯ 5 ⋯ 2 ⋯⟩
median {p6, p4, p3} = 3
{p6, p5, p2, p0} = ? + {0,1,2,4}
⟨⋯ 4 ⋯ 0 ⋯ 5 ⋯⟩
#125034_v2.8
2025-03-07 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
{p5, p4, p0} = ? + {0,1,3}
⟦3,4⟧ ∋ 0
min {p5, p3, p2} = 1
4th → a, 1st → b, |a-b|=5
⛔Avoid
{p4, p3, p0} = ? + {0,1,2}
#125034_v2.8
2025-03-06 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
max ⊢3⊣ = 4
max ⊢1⊣ = 5
⟨? ⋯ 2 ⋯ (?−2) ⋯⟩ (?≠2,4)
⟨ ²ⁿᵈ↓ ¹ˢᵗ↓ ⁰ᵗʰ↓ ⟩ after 3×⟨←⟩
{p6, p4, p1, p0} = ? + {0,1,2,3}
#125034_v2.8
2025-03-06 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 5 ⋯ ? ⋯ 2 (?+1)⟩ (?≠2,1)
Jump(1,2) ≥ 2
⟨ ⁵ᵗʰa ³ʳᵈc ²ⁿᵈb ⟩, a > b > c
#125034_v2.8
2025-03-04 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → 3|4|5
⟨⋯ 0 ⋯ 1 ⋯ 2 ⋯⟩
⟨ ⁵ᵗʰa ³ʳᵈb ⟩, max⟦a,b⟧ = 5
⛔Avoid
⟨ ³ʳᵈa ⁰ᵗʰb ⟩, (ab)₁₀ ≥ 21
⟨⋯ 5 ⋯ ? ⋯ 2 (?+3)⟩ (?≠2)
⟨⋯ ? ⋯ 3 ⋯ (?−2)⟩ (?≠3,5)
Jump(2,3) ≥ 1
#125034_v2.8
2025-03-04 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → a, 0th → b, ab=10
⟨⋯ Perm(1,3) ⋯⟩
6th → a, 0th → b, ab=3+6n
3rd → a, 2nd → b, ab=3+5n
⛔Avoid
3rd → a, 1st → b, a+b=3+5n
#125034_v2.8
2025-03-02 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 2 ⋯ a ⋯⟩, a = 0|1|3|6
5th → a, 1st → b, |a-b|=4
6th → 1|3|4
{p6, p4, p2, p0} = ? + {0,1,2,4}
⛔Avoid
⟨⋯ ? ⋯ 4 ⋯ (?−2)⟩ (?≠4,6)
⟨ ⁴ᵗʰa ¹ˢᵗb ⟩, min⟦a,b⟧ = 0
⟨⋯ Perm(0,2,3) ⋯⟩
#125034_v2.8
2025-03-02 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
0th → 0|1|2
⟨ ⁵ᵗʰa ²ⁿᵈb ⟩, min⟦a,b⟧ = 1
5th → a, 1st → b, a+b=3+5n
⟨? ⋯ 5 (?−2) ⋯ 1 ⋯⟩ (?≠5)
⛔Avoid
⟨ ⁵ᵗʰ↓ ⁴ᵗʰ↓ ³ʳᵈ↑ ²ⁿᵈ↓ ¹ˢᵗ↑ ⁰ᵗʰ↑ ⟩ after 5−⟨⋯⟩
#125034_v2.8
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