Originating from a math proof, 125034 is a game driven by combinatorics, logic, and probability.
2025-06-29 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
1st → 2|4|6
⟨ ▧ ▧ − − ▢ ▢ − ⟩, Σ▧ ≤ Σ▢
4th → a, 1st → b, a+b=0+4n
5th → a, 1st → b, ab=10
⛔Avoid
6th → a, 2nd → b, a+b=3
Sim⟨ ⁶ᵗʰ5 ⁵ᵗʰ4 ⁴ᵗʰ0 ³ʳᵈ3 ²ⁿᵈ1 ¹ˢᵗ6 ⁰ᵗʰ2 ⟩ ≥ 1
⟨ ⁶ᵗʰc ³ʳᵈd ¹ˢᵗb ⁰ᵗʰa ⟩, a > b > c > d
#125034_v2.9
2025-06-27 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(0,4) ≥ 2
3rd → a, 1st → b, ab=5
6th → 5|6
⟨ ⁵ᵗʰb ⁴ᵗʰc ³ʳᵈa ⟩, a > b > c
⛔Avoid
⟨ ²ⁿᵈ↓ ⟩ after 3×⟨→⟩
⟨⋯ 2 ⋯ ? ⋯ 1 (?−2)⟩ (?≠3)
⟨ ⁶ᵗʰa ⁵ᵗʰb ⁴ᵗʰc ²ⁿᵈd ⟩, a > b > c > d
#125034_v2.9
2025-06-27 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → a, 2nd → b, ab=15
2nd → 1|3
⛔Avoid
⟨ − ▧ ▧ − ▢ ▢ ⟩, Σ▧ ≥ Σ▢
⟨⋯ 1 ⋯ 4 ⋯⟩
{p5, p4, p1} = ? + {0,2,3}
#125034_v2.9
2025-06-26 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
4th → a, 1st → b, ab=0
5th|4th|3rd|2nd|1st → 3
5th → a, 3rd → b, a+b=6
Jump(5,6) = 2
⟨? ⋯ 0 (?−1) ⋯ 4 ⋯⟩ (?≠1)
⛔Avoid
min ⊢3⊣ = 3
⟨⋯ 6 ⋯ ? 0 ⋯ (?+1)⟩ (?≠0)
1st → a, 0th → b, ab=3+5n
#125034_v2.9
2025-06-26 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
min ⊢3⊣ = 1
max {p5, p2, p1} = 3
⛔Avoid
⟨ ▧ − − − ▢ ▢ ⟩, ▧ ≤ Σ▢
3rd → 5
#125034_v2.9
2025-06-24 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 2 ⋯ 5 ⋯⟩
⟨ ³ʳᵈa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≤ 243
4th → a, 0th → b, |a-b|=4
5th → a, 1st → b, |a-b|=2
⛔Avoid
⟨⋯ Perm(0,1,5) ⋯⟩
⟨ ▧ ▧ ▧ − ▢ ▢ ⟩, Σ▧ ≤ Σ▢
3rd|1st|0th → 4
#125034_v2.9
2025-06-24 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
min {p6, p2, p0} = 2
⟨ ⁴ᵗʰa ¹ˢᵗb ⟩, max⟦a,b⟧ = 6
5th → a, 2nd → b, |a-b|=1
⟨ ⁶ᵗʰa ²ⁿᵈb ⟩, min⟦a,b⟧ = 1
2nd → a, 0th → b, ab=8
⟨⋯ a ⋯ 3 ⋯⟩, a = 2|6
#125034_v2.9
2025-06-22 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? 2 ⋯ (?−1) ⋯ 4 ⋯⟩ (?≠2,3)
max {p5, p4} = 6
⟨ ³ʳᵈa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≥ 354
⟨ ²ⁿᵈa ¹ˢᵗb ⁰ᵗʰc ⟩, (abc)₁₀ ≥ 215
⛔Avoid
⟨⋯ Perm(0,3,4) ⋯⟩
#125034_v2.9
2025-06-22 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦0,5⟧ ∋ 3,4
{p2, p1, p0} = ? + {0,2,3}
⛔Avoid
⟨⋯ Perm(0,2) ⋯⟩
Sim⟨ ⁵ᵗʰ2 ⁴ᵗʰ5 ³ʳᵈ1 ²ⁿᵈ4 ¹ˢᵗ0 ⁰ᵗʰ3 ⟩ = 1
⟨⋯ Perm(2,4) ⋯⟩
#125034_v2.9
2025-06-19 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(2,6) = 2
Jump(3,5) ≥ 4
2nd → a, 1st → b, |a-b|=3
4th → a, 1st → b, ab=2+5n
⛔Avoid
⟨⋯ 5 ⋯ 2 ⋯ 3 ⋯⟩
#125034_v2.9
2025-06-19 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
Sim⟨ ⁵ᵗʰ1 ⁴ᵗʰ2 ³ʳᵈ0 ²ⁿᵈ5 ¹ˢᵗ4 ⁰ᵗʰ3 ⟩ = 1
2nd → 1|2|3
min ⊢3⊣ = 0
{p5, p3, p2} = ? + {0,1,3}
⛔Avoid
⟨? ⋯ 5 ⋯ (?−1) ⋯⟩ (?≠5)
#125034_v2.9
2025-06-18 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
median {p4, p3, p1} = 1
median {p3, p2, p0} = 4
⟨⋯ 2 ⋯ 6 ⋯ 3 ⋯ 5 ⋯⟩
max ⊢0⊣ ≤ 5
⛔Avoid
6th → a, 4th → b, a+b=1+4n
median {p3, p1, p0} = 3
#125034_v2.9
2025-06-18 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰb ⁴ᵗʰc ⁰ᵗʰa ⟩, a > b > c
{p4, p1, p0} = ? + {0,1,3}
⟨ ²ⁿᵈ↑ ⟩ after 2×⟨→⟩
⟨ − − ▧ − ▢ ▢ ⟩, ▧ ≥ Σ▢
#125034_v2.9
2025-06-16 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 2 ⋯ 0 ⋯ 4 ⋯⟩
median {p5, p2, p1} = 1
Jump(1,3) ≤ 3
5th → a, 3rd → b, a+b=6
⛔Avoid
4th → a, 1st → b, ab=0+5n
#125034_v2.9
2025-06-16 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁶ᵗʰ↑ ⁵ᵗʰ↓ ⁴ᵗʰ↓ ²ⁿᵈ↓ ⟩ after 2×⟨←⟩
⟨⋯ 5 ⋯ 0 ⋯ 3 ⋯⟩
⟨⋯ Perm(1,6) ⋯⟩
⛔Avoid
Sim⟨ ⁶ᵗʰ0 ⁵ᵗʰ6 ⁴ᵗʰ2 ³ʳᵈ4 ²ⁿᵈ3 ¹ˢᵗ5 ⁰ᵗʰ1 ⟩ ≤ 1
6th → a, 2nd → b, a+b=1+6n
{p5, p3, p0} = ? + {0,1,4}
6th → a, 2nd → b, ab=3
#125034_v2.9
2025-06-15 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ ? ⋯ 2 ⋯ (?+5)⟩
⟨ ⁵ᵗʰa ¹ˢᵗb ⟩, min⟦a,b⟧ = 1
⟨⋯ Perm(4,6) ⋯⟩
{p6, p4, p2} = ? + {0,1,4}
3rd → a, 2nd → b, a+b=6
#125034_v2.9
2025-06-15 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 2 ⋯ 3 ⋯⟩
0th → 0|2|4
⟨? ⋯ 3 (?−1) ⋯ 0 ⋯⟩ (?≠3,4)
⟨⋯ 1 ⋯ 3 ⋯ 5 ⋯⟩
#125034_v2.9
2025-06-13 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? ⋯ 6 ⋯ (?−4) ⋯⟩ (?≠6)
{p5, p2, p0} = ? + {0,2,3}
⟨ ⁵ᵗʰa ²ⁿᵈb ⟩, min⟦a,b⟧ = 2
⛔Avoid
⟨⋯ 2 ⋯ a ⋯⟩, a = 3|5|6
⟦0,4⟧ ∋ 2,3,6
⟨ ⁴ᵗʰa ²ⁿᵈb ⁰ᵗʰc ⟩, (abc)₁₀ ≤ 512
median {p6, p3, p1} = 2
#125034_v2.9
2025-06-13 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
2nd → 0|3|5
2nd → 0|3|4
⟨ ⁴ᵗʰa ³ʳᵈb ⁰ᵗʰc ⟩, (abc)₁₀ ≤ 235
0 ∾ 2 ∾ 3 ∾ 5
min ⊢2⊣ ≥ 1
⛔Avoid
{p3, p2, p0} = ? + {0,1,2}
⟨ ⁵ᵗʰa ³ʳᵈb ⟩, min⟦a,b⟧ = 1
⟨ ⁵ᵗʰb ⁴ᵗʰc ⁰ᵗʰa ⟩, a > b > c
Jump(0,1) ≥ 2
#125034_v2.9
2025-06-10 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ▧ − − − ▢ ▢ ⟩, ▧ ≥ Σ▢
⟦0,2⟧ ∋ 4
⟨⋯ 0 ⋯ ? ⋯ 1 (?+3)⟩ (?≠1)
⛔Avoid
⟨ ⁵ᵗʰa ⁴ᵗʰc ¹ˢᵗb ⟩, a > b > c
#125034_v2.9
2025-06-10 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ▧ ▧ ▧ ▢ ▢ ▢ − ⟩, Σ▧ ≤ Σ▢
⟨ ⁶ᵗʰ↑ ⁵ᵗʰ↑ ⁴ᵗʰ= ³ʳᵈ↓ ²ⁿᵈ= ¹ˢᵗ↑ ⁰ᵗʰ↑ ⟩ after 6−⟨⇌⟩
3rd → a, 1st → b, a+b=3+6n
⟨ ⁴ᵗʰa ¹ˢᵗb ⟩, min⟦a,b⟧ = 1
⟨ ⁴ᵗʰa ⁰ᵗʰb ⟩, min⟦a,b⟧ = 0
#125034_v2.9
2025-06-08 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? ⋯ 6 (?−2) ⋯ 2 ⋯⟩ (?≠6)
⟨ ³ʳᵈa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 6
⟦2,3⟧ ∋ 0
⟨⋯ ? ⋯ 5 ⋯ (?−3)⟩ (?≠5)
1st → 5
#125034_v2.9
2025-06-08 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 3 ⋯ 4 ⋯⟩
⟨⋯ Perm(3,4) ⋯⟩
5th → a, 4th → b, |a-b|=1
min {p5, p4, p2} = 1
1st → 1|4|5
⛔Avoid
3rd → a, 0th → b, a+b=5
⟦2,5⟧ ∋ 1,3
Jump(0,3) = 2
1st → a, 0th → b, a+b=7
#125034_v2.9
2025-06-04 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁶ᵗʰa ⁵ᵗʰc ⁰ᵗʰb ⟩, a > b > c
3rd → a, 2nd → b, ab=4+6n
⟨ ⁴ᵗʰa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 5
⛔Avoid
min ⊢3⊣ ≥ 2
⟨ ⁵ᵗʰa ¹ˢᵗb ⟩, max⟦a,b⟧ = 5
min {p4, p2, p0} = 0
3rd → a, 0th → b, a+b=1+5n
⟨⋯ Perm(1,3,5) ⋯⟩
#125034_v2.9
2025-06-04 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ a ⋯ 3 ⋯⟩, a = 0|1|2|4|5
⟨⋯ Perm(0,2) ⋯⟩
Sim⟨ ⁵ᵗʰ0 ⁴ᵗʰ3 ³ʳᵈ4 ²ⁿᵈ2 ¹ˢᵗ5 ⁰ᵗʰ1 ⟩ ≥ 1
2nd → 1|2|5
⟨ ⁴ᵗʰ↑ ²ⁿᵈ↑ ⟩ after 2×⟨←⟩
⛔Avoid
Jump(3,5) = 1
⟨ ⁵ᵗʰ↓ ⁴ᵗʰ↑ ³ʳᵈ↑ ²ⁿᵈ↓ ¹ˢᵗ↓ ⁰ᵗʰ↑ ⟩ after ⟨⇌⟩
⟨ ⁵ᵗʰ↑ ⁴ᵗʰ↓ ³ʳᵈ↓ ²ⁿᵈ↑ ¹ˢᵗ↑ ⁰ᵗʰ↓ ⟩ after ⟨⇌⟩
⟨⋯ Perm(0,4) ⋯⟩
⟨⋯ 2 ⋯ ? 3 ⋯ (?+3)⟩ (?≠0)
3rd → a, 1st → b, a+b=4
#125034_v2.9
2025-06-03 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
{p4, p2, p0} = ? + {0,1,2}
⟦1,4⟧ ∋ 2
⟨ ³ʳᵈb ¹ˢᵗa ⟩, a > b
{p5, p2, p1} = ? + {0,1,3}
#125034_v2.9
2025-06-03 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
max ⊢2⊣ = 5
⟨⋯ ? ⋯ 2 ⋯ (?+3)⟩ (?≠2)
⟨ − − − ▧ ▧ ▢ ▢ ⟩, Σ▧ ≥ Σ▢
5th → a, 1st → b, |a-b|=1
⛔Avoid
⟨ ⁴ᵗʰa ²ⁿᵈb ⟩, (ab)₁₀ ≥ 23
⟨ ³ʳᵈa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 6
⟦1,2⟧ ∋ 0,5
#125034_v2.9
2025-06-01 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
max ⊢2⊣ = 3
⟨ ⁴ᵗʰa ³ʳᵈb ²ⁿᵈc ⟩, a > b > c
6th → a, 1st → b, |a-b|=3
⟨⋯ 5 ⋯ 6 ⋯ 4 ⋯ 0 ⋯⟩
⛔Avoid
0 ∾ 2 ∾ 4 ∾ 6
⟨ ▧ ▧ ▢ ▢ − − − ⟩, Σ▧ ≥ Σ▢
#125034_v2.9
Subscribe to:
Posts (Atom)