Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦4,5⟧ ∋ 3,6
⟨⋯ ? ⋯ 3 ⋯ (?+4)⟩
4th → 4
⟨⋯ 1 ⋯ 6 ⋯⟩
⛔Avoid
Sim⟨ ⁶ᵗʰ4 ⁵ᵗʰ2 ⁴ᵗʰ3 ³ʳᵈ6 ²ⁿᵈ0 ¹ˢᵗ5 ⁰ᵗʰ1 ⟩ ≤ 1
⟨⋯ 1 ⋯ 6 ⋯ 3 ⋯ 5 ⋯⟩
#125034_v2.6
Originating from a math proof, 125034 is a game driven by combinatorics, logic, and probability.
2024-09-29 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th|4th|0th → 4
Sim⟨ ⁵ᵗʰ3 ⁴ᵗʰ4 ³ʳᵈ1 ²ⁿᵈ5 ¹ˢᵗ2 ⁰ᵗʰ0 ⟩ = 0
Jump(2,4) = 2
4th → a, 0th → b, a+b=2+5n
1st → 1|3
#125034_v2.6
2024-09-27 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
4th → a, 3rd → b, a+b=0+5n
6th → a, 0th → b, |a-b|=4
Jump(1,5) = 0
⟨ ³ʳᵈa ²ⁿᵈb ⟩, min⟦a,b⟧ = 2
max ⊢0⊣ ≤ 3
#125034_v2.6
2024-09-27 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰb ²ⁿᵈa ⁰ᵗʰc ⟩, a > b > c
5th → a, 1st → b, a+b=0+5n
⟨⋯ Perm(0,1,5) ⋯⟩
⛔Avoid
⟨? ⋯ 2 ⋯ (?−1) ⋯⟩ (?≠2,3)
⟨? 3 ⋯ (?−2) ⋯ 1 ⋯⟩ (?≠3,5)
#125034_v2.6
2024-09-26 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? 1 ⋯ (?+2) ⋯ 2 ⋯⟩ (?≠1)
5th → a, 3rd → b, ab=0+6n
0 ∾ 1 ∾ 2 ∾ 4 ∾ 5 ∾ 6
0th → 1|2|5
⛔Avoid
⟨⋯ a ⋯ 1 ⋯⟩, a = 2|3|4|6
⟨⋯ ? ⋯ 4 ⋯ (?−1)⟩ (?≠4,5)
#125034_v2.6
2024-09-26 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ a ⋯ 1 ⋯⟩, a = 0|2|3
⟨ ⁴ᵗʰa ¹ˢᵗb ⟩, min⟦a,b⟧ = 0
3rd → a, 1st → b, ab=15
⛔Avoid
⟨ ¹ˢᵗa ⁰ᵗʰb ⟩, (ab)₁₀ ≤ 43
⟨⋯ 4 ⋯ 3 ⋯ 5 ⋯⟩
⟨⋯ 1 ⋯ ? 5 ⋯ (?+4)⟩ (?≠1)
⟨⋯ Perm(0,3,4) ⋯⟩
#125034_v2.6
2024-09-24 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
6th → a, 4th → b, ab=2+6n
⟨⋯ ? ⋯ 0 ⋯ (?+3)⟩ (?≠0)
⟨⋯ 1 ⋯ 4 ⋯ 2 ⋯ 3 ⋯⟩
Sim⟨ ⁶ᵗʰ5 ⁵ᵗʰ4 ⁴ᵗʰ0 ³ʳᵈ2 ²ⁿᵈ1 ¹ˢᵗ6 ⁰ᵗʰ3 ⟩ = 2
⛔Avoid
⟨ ⁶ᵗʰa ⁵ᵗʰb ⟩, max⟦a,b⟧ = 5
⟨⋯ 2 ⋯ ? 6 ⋯ (?+2)⟩ (?≠4)
#125034_v2.6
2024-09-24 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
4th → a, 0th → b, a+b=3
⟨ ²ⁿᵈa ⁰ᵗʰb ⟩, min⟦a,b⟧ = 0
⟦3,4⟧ ∋ 1,5
max ⊢3⊣ = 3
⛔Avoid
⟨⋯ 3 ⋯ ? ⋯ 0 (?−2)⟩ (?≠2)
1st → 4|5
#125034_v2.6
2024-09-22 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ²ⁿᵈb ¹ˢᵗa ⁰ᵗʰc ⟩, a > b > c
⟨⋯ Perm(0,2,4) ⋯⟩
⟨⋯ ? ⋯ 6 ⋯ (?+1)⟩ (?≠5)
5th → a, 2nd → b, a+b=3
3rd → 0|5
⛔Avoid
⟨? ⋯ 0 (?−2) ⋯ 5 ⋯⟩ (?≠2)
#125034_v2.6
2024-09-22 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → a, 0th → b, a+b=2+5n
Jump(2,5) = 2
⟨⋯ 1 ⋯ 3 ⋯⟩
⛔Avoid
min ⊢4⊣ ≥ 1
Sim⟨ ⁵ᵗʰ5 ⁴ᵗʰ4 ³ʳᵈ3 ²ⁿᵈ0 ¹ˢᵗ1 ⁰ᵗʰ2 ⟩ ≥ 2
⟨ ⁵ᵗʰb ³ʳᵈa ⟩, a > b
#125034_v2.6
2024-09-20 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
{p4, p2, p1, p0} = ? + {0,1,2,4}
Jump(5,6) ≥ 2
⟨ ⁴ᵗʰa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 5
⟨ ⁴ᵗʰ↓ ⟩ after ⟨→⟩
0 ∾ 1 ∾ 2 ∾ 5
3rd → a, 1st → b, |a-b|=2
⛔Avoid
6th → a, 4th → b, |a-b|=5
#125034_v2.6
2024-09-20 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
Invariant after 5−⟨⇌⟩
⛔Avoid
⟨⋯ a ⋯ 2 ⋯⟩, a = 3|5
⟨⋯ ? ⋯ 4 ⋯ (?+3)⟩ (?≠1)
⟨⋯ 4 ⋯ 0 ⋯ 3 ⋯⟩
⟨ ⁵ᵗʰa ⁴ᵗʰb ³ʳᵈc ⟩, (abc)₁₀ ≤ 124
#125034_v2.6
2024-09-19 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ²ⁿᵈa ⁰ᵗʰb ⟩, a > b
max ⊢1⊣ = 2
⟨ ⁶ᵗʰ= ⁵ᵗʰ↑ ⁴ᵗʰ↑ ³ʳᵈ↓ ²ⁿᵈ↑ ¹ˢᵗ↑ ⁰ᵗʰ= ⟩ after 6−⟨⇌⟩
⛔Avoid
⟨⋯ a ⋯ 2 ⋯⟩, a = 3|4|5|6
#125034_v2.6
2024-09-19 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ Perm(2,3,4) ⋯⟩
5th|3rd|2nd|1st → 2
5th|4th|3rd|1st → 1
⟨⋯ Perm(1,4,5) ⋯⟩
⛔Avoid
min ⊢5⊣ ≥ 1
#125034_v2.6
2024-09-17 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(0,1) = 4
Jump(1,6) ≥ 3
min ⊢5⊣ = 3
⟨⋯ 3 ⋯ 5 ⋯⟩
⛔Avoid
min ⊢4⊣ ≥ 2
⟨ ⁶ᵗʰa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≥ 123
#125034_v2.6
2024-09-17 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 0 ⋯ 2 ⋯ 4 ⋯⟩
⟨? 3 ⋯ (?−1) ⋯ 0 ⋯⟩ (?≠3,4)
⛔Avoid
Sim⟨ ⁵ᵗʰ4 ⁴ᵗʰ1 ³ʳᵈ3 ²ⁿᵈ5 ¹ˢᵗ2 ⁰ᵗʰ0 ⟩ ≤ 1
#125034_v2.6
2024-09-15 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
4th → a, 2nd → b, a+b=3+6n
2nd → a, 1st → b, |a-b|=3
⛔Avoid
Sim⟨ ⁶ᵗʰ5 ⁵ᵗʰ3 ⁴ᵗʰ0 ³ʳᵈ4 ²ⁿᵈ6 ¹ˢᵗ2 ⁰ᵗʰ1 ⟩ ≤ 1
⟨⋯ a ⋯ 2 ⋯⟩, a = 0|1|6
⟨ ³ʳᵈa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 4
min ⊢4⊣ ≤ 2
#125034_v2.6
2024-09-15 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁴ᵗʰa ³ʳᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≥ 350
1st → 2|3
0th → 0|1
5th → a, 4th → b, a+b=3+4n
⛔Avoid
⟨⋯ 5 ⋯ a ⋯⟩, a = 1|3|4
#125034_v2.6
2024-09-13 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨? ⋯ 0 (?+1) ⋯ 5 ⋯⟩ (?≠0)
⟨ ⁶ᵗʰa ²ⁿᵈc ⁰ᵗʰb ⟩, a > b > c
⟨⋯ Perm(0,4,6) ⋯⟩
⟨⋯ 0 ⋯ ? ⋯ 5 (?+2)⟩ (?≠3)
⛔Avoid
⟦0,2⟧ ∋ 1,4,5,6
#125034_v2.6
2024-09-13 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(3,5) = 0
4th → a, 0th → b, ab=0+5n
⟨⋯ ? ⋯ 4 ⋯ (?−3)⟩ (?≠4)
⟨ ⁴ᵗʰc ³ʳᵈb ²ⁿᵈa ⟩, a > b > c
⛔Avoid
⟨⋯ 5 ⋯ 0 ⋯⟩
#125034_v2.6
2024-09-12 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁶ᵗʰc ⁵ᵗʰb ¹ˢᵗa ⟩, a > b > c
⟨⋯ 5 ⋯ 3 ⋯ 0 ⋯ 1 ⋯⟩
⛔Avoid
Jump(0,4) ≥ 1
3rd → 2|4|5
#125034_v2.6
2024-09-12 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → a, 0th → b, ab=8
⟨ ⁵ᵗʰa ⁴ᵗʰb ¹ˢᵗc ⟩, (abc)₁₀ ≥ 251
⛔Avoid
⟨⋯ a ⋯ 2 ⋯⟩, a = 0|1|3
⟨⋯ ? ⋯ 1 ⋯ (?+1)⟩ (?≠1,0)
⟨ ⁵ᵗʰa ³ʳᵈb ²ⁿᵈc ⟩, (abc)₁₀ ≤ 203
#125034_v2.6
2024-09-10 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁶ᵗʰa ³ʳᵈb ⟩, a > b
4th → a, 3rd → b, ab=2+4n
⟨ ²ⁿᵈa ⁰ᵗʰb ⟩, min⟦a,b⟧ = 2
⟨ ²ⁿᵈa ¹ˢᵗb ⁰ᵗʰc ⟩, (abc)₁₀ ≤ 510
2nd → a, 1st → b, |a-b|=1
⛔Avoid
⟨ ⁶ᵗʰ↑ ²ⁿᵈ↑ ⁰ᵗʰ↓ ⟩ after 2×⟨←⟩
Sim⟨ ⁶ᵗʰ5 ⁵ᵗʰ0 ⁴ᵗʰ3 ³ʳᵈ4 ²ⁿᵈ1 ¹ˢᵗ2 ⁰ᵗʰ6 ⟩ ≥ 2
#125034_v2.6
2024-09-10 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰa ³ʳᵈb ²ⁿᵈc ⟩, (abc)₁₀ ≤ 105
Jump(1,5) = 2
⛔Avoid
min ⊢4⊣ ≥ 1
3rd|1st|0th → 3
max ⊢3⊣ = 3
#125034_v2.6
2024-09-08 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
{p6, p4, p3, p2} = ? + {0,2,3,4}
⟨ ⁴ᵗʰb ³ʳᵈa ²ⁿᵈc ⟩, a > b > c
⟨ ⁶ᵗʰa ³ʳᵈb ⟩, min⟦a,b⟧ = 2
Sim⟨ ⁶ᵗʰ0 ⁵ᵗʰ4 ⁴ᵗʰ5 ³ʳᵈ1 ²ⁿᵈ3 ¹ˢᵗ2 ⁰ᵗʰ6 ⟩ = 0
⛔Avoid
⟨ ⁵ᵗʰb ⁴ᵗʰa ⟩, a > b
5th → a, 1st → b, ab=30
⟨ ⁶ᵗʰa ²ⁿᵈb ⟩, (ab)₁₀ ≤ 30
#125034_v2.6
2024-09-08 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
max ⊢0⊣ = 5
⟨⋯ 4 ⋯ 5 ⋯⟩
⟨ ⁴ᵗʰb ⁰ᵗʰa ⟩, a > b
2nd → 1
⛔Avoid
5th|4th|3rd|0th → 3
#125034_v2.6
2024-09-06 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
max ⊢3⊣ ≤ 4
⟨? ⋯ 6 (?−2) ⋯ 1 ⋯⟩ (?≠6)
6th|4th|2nd|0th → 0
⟨⋯ Perm(0,5) ⋯⟩
⛔Avoid
⟨⋯ a ⋯ 5 ⋯⟩, a = 4|6
⟨ ⁵ᵗʰa ²ⁿᵈb ⟩, max⟦a,b⟧ = 6
#125034_v2.6
2024-09-06 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
0 ∾ 1
4th → a, 3rd → b, a+b=4+5n
⟦1,5⟧ ∋ 2
4th|3rd|2nd|0th → 4
⛔Avoid
4th → a, 1st → b, a+b=6
⟨⋯ Perm(1,2,3) ⋯⟩
3rd → 0|1|2|4
#125034_v2.6
2024-09-05 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
min ⊢4⊣ = 1
⟦2,4⟧ ∋ 0,1,3
4th → 3
0th → 3|6
⛔Avoid
6th → a, 0th → b, a+b=10
2nd → 1
#125034_v2.6
2024-09-05 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
4th → a, 3rd → b, |a-b|=4
⟨⋯ Perm(1,4) ⋯⟩
3rd → a, 1st → b, a+b=2+4n
⛔Avoid
5th|4th|2nd → 4
Jump(0,3) = 0
#125034_v2.6
2024-09-03 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰd ⁴ᵗʰc ²ⁿᵈb ¹ˢᵗa ⟩, a > b > c > d
4th → a, 0th → b, a+b=3+5n
⛔Avoid
6th|5th|2nd|1st|0th → 5
⟨⋯ 2 ⋯ 3 ⋯⟩
{p6, p5, p4, p0} = ? + {0,1,2,3}
⟨ ⁶ᵗʰa ⁵ᵗʰc ¹ˢᵗb ⟩, a > b > c
#125034_v2.6
2024-09-03 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → a, 4th → b, ab=3
⛔Avoid
⟨⋯ a ⋯ 3 ⋯⟩, a = 1|5
⟨ ⁵ᵗʰa ²ⁿᵈb ⁰ᵗʰc ⟩, (abc)₁₀ ≥ 324
2nd → a, 1st → b, ab=0+5n
#125034_v2.6
2024-09-01 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦0,6⟧ ∋ 2,4
4th → a, 2nd → b, a+b=1+6n
3rd → a, 1st → b, |a-b|=4
⟨ ³ʳᵈ↓ ²ⁿᵈ↓ ¹ˢᵗ↓ ⁰ᵗʰ↓ ⟩ after 2×⟨→⟩
⛔Avoid
⟨? ⋯ 3 ⋯ (?+1) ⋯⟩ (?≠3,2)
#125034_v2.6
2024-09-01 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦3,4⟧ ∋ 0,2,5
⛔Avoid
⟦1,5⟧ ∋ 0,2
⟨⋯ 3 ⋯ a ⋯⟩, a = 0|1|4|5
max ⊢2⊣ ≥ 3
1st → 2|4|5
#125034_v2.6
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