Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → a, 2nd → b, a+b=4+5n
max ⊢1⊣ = 4
⛔Avoid
⟨ ▧ ▧ − − − ▢ ⟩, Σ▧ ≥ ▢
⟨ ⁵ᵗʰa ³ʳᵈb ²ⁿᵈc ⟩, (abc)₁₀ ≤ 310
#125034_v2.9
Originating from a math proof, 125034 is a game driven by combinatorics, logic, and probability.
2025-04-27 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦0,3⟧ ∋ 2,4,5
{p3, p2, p1, p0} = ? + {0,1,2,4}
Jump(0,1) = 3
⟦0,1⟧ ∋ 2,6
⛔Avoid
max ⊢0⊣ = 4
#125034_v2.8
2025-04-27 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ Perm(0,1,2) ⋯⟩
5th → a, 3rd → b, a+b=8
⟨ ⁵ᵗʰa ²ⁿᵈb ⁰ᵗʰc ⟩, (abc)₁₀ ≥ 302
⛔Avoid
4th → a, 2nd → b, a+b=1+5n
2nd → a, 1st → b, |a-b|=1
#125034_v2.8
2025-04-25 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 5 ⋯ 6 ⋯ 1 ⋯⟩
4th → 0|3|6
5th → a, 3rd → b, ab=0
{p4, p2, p0} = ? + {0,2,3}
⟨ ³ʳᵈ↓ ¹ˢᵗ↑ ⟩ after ⟨→⟩
#125034_v2.8
2025-04-25 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? ⋯ 4 (?+1) ⋯ 2 ⋯⟩ (?≠4,3)
4th → a, 2nd → b, ab=2+5n
⟨ ⁵ᵗʰc ⁴ᵗʰa ³ʳᵈb ⟩, a > b > c
⟨⋯ ? ⋯ 3 ⋯ (?−1)⟩ (?≠3,4)
#125034_v2.8
2025-04-24 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
{p5, p3, p2, p0} = ? + {0,1,2,3}
Jump(0,6) = 1
Jump(0,5) ≥ 1
3rd → 0|2|3|4|5
⟨? ⋯ 5 ⋯ (?+2) ⋯⟩ (?≠3)
⛔Avoid
max ⊢3⊣ ≥ 5
#125034_v2.8
2025-04-24 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
4th → a, 3rd → b, a+b=3
⟨ ⁴ᵗʰc ³ʳᵈa ²ⁿᵈb ⟩, a > b > c
5th → 0|1|3|5
⛔Avoid
⟨ ⁵ᵗʰa ¹ˢᵗb ⁰ᵗʰc ⟩, (abc)₁₀ ≥ 325
4th → a, 0th → b, |a-b|=5
#125034_v2.8
2025-04-21 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
max ⊢0⊣ ≤ 4
⟨⋯ a ⋯ 5 ⋯⟩, a = 1|2|3
4th → a, 3rd → b, |a-b|=2
median {p4, p3, p2} = 1
⛔Avoid
⟦3,5⟧ ∋ 0,1,2
{p5, p4, p3} = ? + {0,1,2}
⟨ ⁵ᵗʰ↓ ⁴ᵗʰ↑ ³ʳᵈ↑ ²ⁿᵈ↑ ¹ˢᵗ↓ ⁰ᵗʰ↓ ⟩ after 5−⟨⋯⟩
#125034_v2.8
2025-04-21 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, ab=2+5n
min {p4, p2, p1} = 1
min ⊢5⊣ = 2
⛔Avoid
5th → a, 3rd → b, |a-b|=2
1st → 0|2|4|5|6
⟨⋯ 6 ⋯ a ⋯⟩, a = 1|2|4|5
#125034_v2.8
2025-04-20 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁶ᵗʰ↑ ⁵ᵗʰ↑ ⁴ᵗʰ↓ ³ʳᵈ↓ ²ⁿᵈ↓ ¹ˢᵗ↑ ⁰ᵗʰ↑ ⟩ after 6−⟨⇌⟩
Jump(2,3) = 3
{p5, p2, p1, p0} = ? + {0,1,2,3}
5th → a, 0th → b, |a-b|=2
⟨ ⁶ᵗʰa ¹ˢᵗb ⟩, (ab)₁₀ ≤ 40
⛔Avoid
⟨ ⁴ᵗʰb ³ʳᵈa ⟩, a > b
3rd → a, 2nd → b, |a-b|=1
#125034_v2.8
2025-04-20 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰa ⁰ᵗʰb ⟩, a > b
Jump(2,3) = 0
Jump(0,1) = 2
⛔Avoid
⟨⋯ Perm(0,2,3) ⋯⟩
Jump(0,5) = 0
⟨? ⋯ 4 ⋯ (?−2) ⋯⟩ (?≠4)
#125034_v2.8
2025-04-18 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Sim⟨ ⁶ᵗʰ4 ⁵ᵗʰ1 ⁴ᵗʰ5 ³ʳᵈ3 ²ⁿᵈ2 ¹ˢᵗ0 ⁰ᵗʰ6 ⟩ ≤ 1
6th|5th|3rd|0th → 6
{p6, p4, p3, p2} = ? + {0,1,2,3}
{p6, p1, p0} = ? + {0,1,3}
⟨ ⁴ᵗʰ↓ ³ʳᵈ↓ ²ⁿᵈ↑ ¹ˢᵗ↑ ⟩ after 2×⟨→⟩
#125034_v2.8
2025-04-18 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
{p4, p3, p0} = ? + {0,1,2}
5th → a, 0th → b, a+b=1
⛔Avoid
2nd → a, 0th → b, a+b=1+4n
median {p4, p2, p0} = 3
#125034_v2.8
2025-04-17 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
median {p6, p3, p1} = 4
⛔Avoid
6th → a, 0th → b, ab=4+6n
⟨⋯ 1 ⋯ a ⋯⟩, a = 0|2|3|4|6
⟨⋯ a ⋯ 4 ⋯⟩, a = 0|2|6
⟨⋯ ? ⋯ 0 ⋯ (?+2)⟩ (?≠0)
Jump(2,5) ≥ 3
#125034_v2.8
2025-04-17 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
2nd → a, 1st → b, a+b=1
⟨ ²ⁿᵈa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 4
2nd → a, 0th → b, |a-b|=4
⛔Avoid
Jump(3,5) = 1
⟨ ³ʳᵈa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 4
#125034_v2.8
2025-04-15 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
{p4, p2, p1} = ? + {0,1,2}
⟨⋯ Perm(0,1,4) ⋯⟩
3rd → a, 2nd → b, a+b=3
⛔Avoid
4th → a, 2nd → b, ab=0+4n
#125034_v2.8
2025-04-15 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ³ʳᵈa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 4
⟨ ⁴ᵗʰa ³ʳᵈb ¹ˢᵗc ⟩, a > b > c
5th|4th|3rd|2nd|1st → 6
min {p6, p5, p0} = 0
⟨⋯ a ⋯ 0 ⋯⟩, a = 1|2|3|4
⛔Avoid
max ⊢3⊣ ≤ 5
⟨ ⁴ᵗʰb ²ⁿᵈa ⁰ᵗʰc ⟩, a > b > c
Jump(0,4) = 2
4th → a, 2nd → b, |a-b|=2
#125034_v2.8
2025-04-13 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? ⋯ 3 (?−2) ⋯ 4 ⋯⟩ (?≠3,5)
⟨ ⁶ᵗʰ↑ ⁴ᵗʰ↑ ²ⁿᵈ↑ ⁰ᵗʰ↑ ⟩ after 3×⟨←⟩
#125034_v2.8
2025-04-13 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ³ʳᵈa ¹ˢᵗb ⟩, (ab)₁₀ ≤ 32
⟨⋯ ? ⋯ 3 ⋯ (?+1)⟩ (?≠3,2)
5th → a, 0th → b, a+b=6
{p3, p1, p0} = ? + {0,2,3}
⛔Avoid
⟨ ³ʳᵈa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 5
#125034_v2.8
2025-04-11 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|=6
5th → a, 3rd → b, ab=24
median {p4, p1, p0} = 3
6th → a, 1st → b, ab=5
#125034_v2.8
2025-04-11 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
4th → a, 0th → b, a+b=0+5n
⟨⋯ ? ⋯ 2 ⋯ (?−2)⟩ (?≠2,4)
⛔Avoid
median {p5, p2, p1} = 3
⟨⋯ 0 ⋯ ? ⋯ 2 (?−2)⟩ (?≠2,4)
⟨⋯ Perm(0,1,4) ⋯⟩
Jump(4,5) = 0
#125034_v2.8
2025-04-08 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
1st → a, 0th → b, a+b=3+4n
⟨ ³ʳᵈb ²ⁿᵈa ¹ˢᵗc ⟩, a > b > c
⛔Avoid
⟨ ¹ˢᵗa ⁰ᵗʰb ⟩, a > b
⟨ ⁴ᵗʰa ³ʳᵈb ⁰ᵗʰc ⟩, (abc)₁₀ ≤ 254
3rd|2nd|1st|0th → 3
#125034_v2.8
2025-04-08 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 3 ⋯ 6 ⋯ 2 ⋯⟩
max {p6, p3, p0} = 4
min ⊢5⊣ = 1
⟨⋯ Perm(0,4,6) ⋯⟩
⟨ ⁴ᵗʰ↑ ⁰ᵗʰ↓ ⟩ after 3×⟨←⟩
⛔Avoid
max ⊢2⊣ ≥ 5
#125034_v2.8
2025-04-06 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ Perm(1,2,5) ⋯⟩
⟨⋯ Perm(0,3,4) ⋯⟩
⟨⋯ Perm(5,6) ⋯⟩
⛔Avoid
Jump(2,3) ≥ 2
⟨ ⁶ᵗʰa ⁵ᵗʰb ³ʳᵈc ⟩, a > b > c
3rd|1st → 2
max {p5, p4} = 3
#125034_v2.8
2025-04-06 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 2 ⋯ ? ⋯ 5 (?+2)⟩ (?≠3)
4th → a, 0th → b, a+b=2+5n
5th → a, 0th → b, |a-b|=4
⛔Avoid
⟨? ⋯ 1 ⋯ (?+2) ⋯⟩ (?≠1)
#125034_v2.8
2025-04-04 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → 0|1|4
⟨ ⁶ᵗʰ↓ ⁵ᵗʰ↓ ⁴ᵗʰ↑ ³ʳᵈ= ²ⁿᵈ↓ ¹ˢᵗ↑ ⁰ᵗʰ↑ ⟩ after ⟨⇌⟩
⟨ ³ʳᵈa ⁰ᵗʰb ⟩, min⟦a,b⟧ = 1
{p5, p4, p2} = ? + {0,1,3}
#125034_v2.8
2025-04-04 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ Perm(0,3,5) ⋯⟩
3rd → a, 0th → b, a+b=2+5n
⛔Avoid
Jump(0,2) = 0
0th → 3
⟨⋯ a ⋯ 2 ⋯⟩, a = 1|4|5
⟨? ⋯ 5 ⋯ (?−2) ⋯⟩ (?≠5)
#125034_v2.8
2025-04-03 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
4th → 3
⟨ ⁵ᵗʰb ³ʳᵈa ²ⁿᵈc ⟩, a > b > c
⟨ ⁵ᵗʰa ⁴ᵗʰb ³ʳᵈc ⟩, (abc)₁₀ ≥ 436
⛔Avoid
⟨⋯ 6 ⋯ 1 ⋯⟩
4th → a, 0th → b, a+b=3+5n
⟨⋯ 1 ⋯ ? ⋯ 0 (?−4)⟩ (?≠4)
6th|5th|3rd|2nd|0th → 0
#125034_v2.8
2025-04-03 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰc ⁴ᵗʰa ²ⁿᵈb ⟩, a > b > c
2nd → a, 1st → b, ab=1+4n
⟦3,4⟧ ∋ 1,5
⛔Avoid
⟨⋯ Perm(0,2,3) ⋯⟩
⟨⋯ 0 ⋯ ? 2 ⋯ (?+3)⟩ (?≠2)
#125034_v2.8
2025-04-01 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
Sim⟨ ⁵ᵗʰ0 ⁴ᵗʰ2 ³ʳᵈ5 ²ⁿᵈ4 ¹ˢᵗ1 ⁰ᵗʰ3 ⟩ ≤ 1
min ⊢4⊣ ≤ 1
⟨⋯ 0 ⋯ a ⋯⟩, a = 2|3
5th → 0|2|4
⟨ ⁴ᵗʰa ¹ˢᵗb ⟩, max⟦a,b⟧ = 5
⛔Avoid
{p4, p1, p0} = ? + {0,1,2}
⟨? 5 ⋯ (?+1) ⋯ 1 ⋯⟩ (?≠4)
1st → a, 0th → b, |a-b|=2
Jump(3,4) ≥ 2
max ⊢4⊣ = 4
#125034_v2.8
2025-04-01 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Sim⟨ ⁶ᵗʰ2 ⁵ᵗʰ0 ⁴ᵗʰ6 ³ʳᵈ3 ²ⁿᵈ5 ¹ˢᵗ4 ⁰ᵗʰ1 ⟩ = 2
{p6, p4, p3} = ? + {0,1,2}
⟦2,4⟧ ∋ 1,3
{p6, p5, p3, p0} = ? + {0,1,2,3}
⛔Avoid
⟨⋯ 5 ⋯ ? ⋯ 6 (?−1)⟩ (?≠6)
#125034_v2.8
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