Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
6th → a, 5th → b, a+b=5
Jump(0,6) = 0
⟨⋯ Perm(4,5,6) ⋯⟩
⟨⋯ 2 ⋯ ? 1 ⋯ (?−2)⟩ (?≠3)
⛔Avoid
⟨? ⋯ 1 (?+2) ⋯ 0 ⋯⟩ (?≠1)
#125034_v2.1
Originating from a math proof, 125034 is a game driven by combinatorics, logic, and probability.
2023-10-31 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → a, 0th → b, |a-b|=3
2nd → a, 0th → b, ab=3+5n
⟨⋯ a ⋯ 1 ⋯⟩, a = 0|2|5
⟨ ⁵ᵗʰ= ⁴ᵗʰ↑ ³ʳᵈ↓ ²ⁿᵈ↓ ¹ˢᵗ↑ ⁰ᵗʰ= ⟩ after 5−⟨⇌⟩
#125034_v2.1
2023-10-29 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(0,5) = 3
⟨⋯ 2 ⋯ ? 3 ⋯ (?+3)⟩ (?≠3,0)
6th|5th|4th|3rd → 5
⛔Avoid
⟨⋯ ? ⋯ 6 ⋯ (?+3)⟩ (?≠3)
⟦4,5⟧ ∋ 1,2,3
#125034_v2.1
2023-10-29 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦2,5⟧ ∋ 3,4
⟨ ⁴ᵗʰb ²ⁿᵈa ⁰ᵗʰc ⟩, a > b > c
⟨ ⁵ᵗʰ↑ ⁴ᵗʰ↑ ³ʳᵈ↓ ²ⁿᵈ↑ ¹ˢᵗ↓ ⁰ᵗʰ↓ ⟩ after ⟨⇌⟩
#125034_v2.1
2023-10-27 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰb ⁴ᵗʰc ⁰ᵗʰa ⟩, a > b > c
⟨? ⋯ 2 ⋯ (?−2) ⋯⟩ (?≠2,4)
Jump(0,5) = 0
⟨⋯ 3 ⋯ ? 6 ⋯ (?+4)⟩ (?≠2)
⛔Avoid
⟨⋯ Perm(0,4,6) ⋯⟩
#125034_v2.1
2023-10-27 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → 1|2|5
4th → 4
⛔Avoid
1st → 1|3|4|5
2nd → 2|4|5
⟨ ³ʳᵈ↓ ⟩ after ⟨←⟩
⟨⋯ 3 ⋯ 0 ⋯⟩
#125034_v2.1
2023-10-25 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦1,4⟧ ∋ 0,3
0 ∾ 2 ∾ 4 ∾ 5 ∾ 6
⟨ ⁴ᵗʰc ¹ˢᵗb ⁰ᵗʰa ⟩, a > b > c
⛔Avoid
⟨⋯ a ⋯ 4 ⋯⟩, a = 0|1|2|3
4th|3rd|2nd|1st|0th → 6
2nd → a, 1st → b, |a-b|=2
#125034_v2.1
2023-10-25 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th|4th|3rd|0th → 5
4th → a, 1st → b, |a-b|=1
⟨⋯ Perm(2,4,5) ⋯⟩
⟨ ⁵ᵗʰa ²ⁿᵈb ⁰ᵗʰc ⟩, (abc)₁₀ ≤ 341
5th → a, 0th → b, a+b=3+5n
⛔Avoid
⟨⋯ a ⋯ 1 ⋯⟩, a = 0|2|4
#125034_v2.1
Q1(m=6) 2023-10-23
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 3 ⋯ ? 5 ⋯ (?−2)⟩ (?≠5)
⟨⋯ 3 ⋯ ? 0 ⋯ (?+1)⟩ (?≠0)
⟨⋯ 3 ⋯ 1 ⋯⟩
6th → a, 1st → b, a+b=3+5n
⛔Avoid
⟦1,3⟧ ∋ 0
⟨⋯ a ⋯ 0 ⋯⟩, a = 2|4|6
#125034_v2.0
WR 2023-10-22
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(2,4) = 1
⟨ ⁵ᵗʰa ⁴ᵗʰb ⟩, (ab)₁₀ ≥ 24
4th → a, 1st → b, a+b=0+5n
⛔Avoid
⟦3,4⟧ ∋ 0
5th|4th|2nd|0th → 4
⟨⋯ 3 ⋯ a ⋯⟩, a = 0|4
#125034_v2.0
Q1(m=6) 2023-10-22
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
2nd → a, 1st → b, a+b=3
5th → a, 3rd → b, a+b=10
Sim⟨ ⁶ᵗʰ2 ⁵ᵗʰ5 ⁴ᵗʰ0 ³ʳᵈ4 ²ⁿᵈ3 ¹ˢᵗ6 ⁰ᵗʰ1 ⟩ = 3
3rd → 0|1|2|3|4
⟨⋯ 5 ⋯ a ⋯⟩, a = 0|1|2|3|4|6
⛔Avoid
⟨⋯ 5 ⋯ 6 ⋯ 2 ⋯⟩
#125034_v2.0
Q1(m=6) 2023-10-20
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → a, 1st → b, ab=3+6n
⟨ ⁵ᵗʰc ⁴ᵗʰa ⁰ᵗʰb ⟩, a > b > c
⟨⋯ Perm(4,5) ⋯⟩
⟨⋯ 0 ⋯ ? 1 ⋯ (?+4)⟩ (?≠1)
#125034_v2.0
WR 2023-10-20
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁴ᵗʰa ³ʳᵈb ⁰ᵗʰc ⟩, (abc)₁₀ ≥ 415
3rd → 0|4
5th → a, 0th → b, |a-b|=3
⛔Avoid
⟨ ⁵ᵗʰa ⁴ᵗʰb ⁰ᵗʰc ⟩, (abc)₁₀ ≤ 250
⟨⋯ Perm(3,4,5) ⋯⟩
5th → a, 1st → b, ab=8
#125034_v2.0
Q1(m=6) 2023-10-19
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 ⟨⇌⟩
⟨⋯ ? ⋯ 1 ⋯ (?−4)⟩ (?≠5)
5th → a, 1st → b, a+b=5+6n
⛔Avoid
⟨? ⋯ 4 ⋯ (?+4) ⋯⟩ (?≠0)
4th → 1|2|6
5th → a, 2nd → b, ab=2+4n
⟨⋯ a ⋯ 2 ⋯⟩, a = 1|3
#125034_v2.0
WR 2023-10-19
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ Perm(0,4,5) ⋯⟩
⛔Avoid
⟨⋯ 2 ⋯ 3 ⋯⟩
2nd → a, 1st → b, |a-b|=4
⟨ ²ⁿᵈa ¹ˢᵗb ⟩, (ab)₁₀ ≥ 21
Jump(0,1) ≤ 1
Sim⟨ ⁵ᵗʰ4 ⁴ᵗʰ0 ³ʳᵈ2 ²ⁿᵈ1 ¹ˢᵗ3 ⁰ᵗʰ5 ⟩ ≥ 1
#125034_v2.0
Q1(m=6) 2023-10-18
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → a, 0th → b, ab=4+6n
⟨ ⁶ᵗʰd ⁵ᵗʰc ²ⁿᵈa ¹ˢᵗb ⟩, a > b > c > d
Jump(2,5) = 4
⟨⋯ 0 ⋯ ? 6 ⋯ (?+2)⟩ (?≠4)
⛔Avoid
4th → 1|2|4|5
#125034_v2.0
WR 2023-10-17
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦4,5⟧ ∋ 0,3
⟨? ⋯ 3 ⋯ (?−2) ⋯⟩ (?≠3,5)
4th → a, 0th → b, |a-b|=2
3rd → a, 0th → b, |a-b|=1
⛔Avoid
⟨⋯ Perm(0,3,4) ⋯⟩
3rd → a, 2nd → b, a+b=2+5n
#125034_v2.0
Q1(m=6) 2023-10-17
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
6th → a, 2nd → b, a+b=1+5n
Jump(1,4) ≥ 2
6th → a, 1st → b, |a-b|=1
5th → a, 3rd → b, |a-b|=1
⟨⋯ 2 ⋯ 0 ⋯⟩
⟦0,6⟧ ∋ 4,5
#125034_v2.0
Q1(m=6) 2023-10-15
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → 0|1|5
4th → a, 0th → b, a+b=3+4n
⟨ ⁴ᵗʰ↑ ²ⁿᵈ↓ ¹ˢᵗ↓ ⁰ᵗʰ↓ ⟩ after 3×⟨←⟩
6th → a, 0th → b, a+b=3+6n
Jump(0,4) = 1
#125034_v2.0
WR 2023-10-15
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ ? ⋯ 4 ⋯ (?−2)⟩ (?≠4)
5th → a, 2nd → b, a+b=5
⟨ ²ⁿᵈa ¹ˢᵗb ⁰ᵗʰc ⟩, (abc)₁₀ ≥ 423
5th|4th|3rd|2nd → 4
⛔Avoid
⟨⋯ ? ⋯ 2 ⋯ (?−1)⟩ (?≠2,3)
#125034_v2.0
Q1(m=6) 2023-10-13
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
1st → a, 0th → b, ab=0+5n
⟨⋯ ? ⋯ 5 ⋯ (?+2)⟩ (?≠3)
5th → a, 2nd → b, |a-b|=1
⟨ ⁶ᵗʰa ⁴ᵗʰb ³ʳᵈc ⟩, (abc)₁₀ ≤ 125
5th → a, 4th → b, a+b=5
⛔Avoid
Jump(1,4) ≥ 1
⟨ ⁶ᵗʰc ⁵ᵗʰa ⁰ᵗʰb ⟩, a > b > c
4th|3rd|1st|0th → 4
⟨ ⁵ᵗʰb ⁴ᵗʰd ³ʳᵈc ⁰ᵗʰa ⟩, a > b > c > d
#125034_v2.0
WR 2023-10-13
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 3 ⋯ 4 ⋯ 1 ⋯⟩
⟨⋯ ? ⋯ 5 ⋯ (?−1)⟩ (?≠5)
3rd → 3|4|5
⛔Avoid
⟨ ⁵ᵗʰa ²ⁿᵈc ¹ˢᵗb ⟩, a > b > c
5th → a, 3rd → b, a+b=0+5n
5th|3rd|2nd|1st → 5
#125034_v2.0
Q1(m=6) 2023-10-12
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 5 ⋯ ? 4 ⋯ (?−4)⟩ (?≠4)
5th → a, 4th → b, |a-b|=5
⟨? 0 ⋯ (?+5) ⋯ 6 ⋯⟩ (?≠0)
⛔Avoid
3rd → 6
#125034_v2.0
WR 2023-10-12
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁴ᵗʰa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≥ 302
⟨ ³ʳᵈc ²ⁿᵈb ⁰ᵗʰa ⟩, a > b > c
⛔Avoid
⟨⋯ 0 ⋯ a ⋯⟩, a = 1|3
⟨ ³ʳᵈb ²ⁿᵈa ¹ˢᵗc ⟩, a > b > c
⟦1,5⟧ ∋ 4
#125034_v2.0
Q1(m=6) 2023-10-10
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦0,1⟧ ∋ 3,5
⟨⋯ 5 ⋯ 6 ⋯⟩
⟨? 4 ⋯ (?+3) ⋯ 1 ⋯⟩ (?≠1)
⟨ ⁵ᵗʰa ³ʳᵈb ²ⁿᵈc ⟩, (abc)₁₀ ≤ 425
Jump(0,6) ≤ 4
⛔Avoid
Jump(3,6) = 2
#125034_v2.0
WR 2023-10-10
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦4,5⟧ ∋ 2,3
Jump(1,2) ≥ 2
5th → a, 1st → b, ab=0
⟨⋯ Perm(0,2,5) ⋯⟩
⛔Avoid
5th|3rd → 2
#125034_v2.0
Q1(m=6) 2023-10-09
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰc ³ʳᵈa ²ⁿᵈd ⁰ᵗʰb ⟩, a > b > c > d
⟨⋯ 2 ⋯ ? 6 ⋯ (?−2)⟩ (?≠6)
5th → a, 3rd → b, |a-b|=5
#125034_v2.0
Q1(m=6) 2023-10-08
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
6th → a, 4th → b, ab=2
⟨⋯ Perm(0,1,3) ⋯⟩
Jump(0,3) ≥ 1
⟨ ⁴ᵗʰa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≤ 150
⛔Avoid
6th → a, 0th → b, ab=10
3rd → 0|4
#125034_v2.0
WR 2023-10-08
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 0 ⋯ 4 ⋯⟩
5th → 1|2|3
⟨ ⁰ᵗʰ↑ ⟩ after 2×⟨→⟩
⛔Avoid
⟨⋯ 5 ⋯ a ⋯⟩, a = 1|3
5th → a, 1st → b, a+b=8
3rd|1st → 4
⟨⋯ Perm(3,4,5) ⋯⟩
Jump(4,5) = 1
#125034_v2.0
Q1(m=6) 2023-10-06
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ Perm(2,5,6) ⋯⟩
⟨⋯ 5 ⋯ ? ⋯ 3 (?−1)⟩ (?≠3,4)
6th → 1|4|5
4th → a, 2nd → b, ab=2+4n
Jump(3,6) = 1
⛔Avoid
Sim⟨ ⁶ᵗʰ4 ⁵ᵗʰ3 ⁴ᵗʰ2 ³ʳᵈ5 ²ⁿᵈ1 ¹ˢᵗ6 ⁰ᵗʰ0 ⟩ ≥ 1
#125034_v2.0
WR 2023-10-06
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≥ 413
2nd → a, 0th → b, ab=1+5n
⛔Avoid
5th → a, 1st → b, |a-b|=1
Sim⟨ ⁵ᵗʰ5 ⁴ᵗʰ0 ³ʳᵈ3 ²ⁿᵈ2 ¹ˢᵗ4 ⁰ᵗʰ1 ⟩ ≥ 2
⟨⋯ Perm(0,3) ⋯⟩
⟦2,4⟧ ∋ 1,3,5
#125034_v2.0
Q1(m=6) 2023-10-05
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰc ⁴ᵗʰa ²ⁿᵈd ⁰ᵗʰb ⟩, a > b > c > d
3rd → a, 0th → b, |a-b|=1
⟨? ⋯ 2 ⋯ (?+2) ⋯⟩ (?≠2,0)
⛔Avoid
⟨ ³ʳᵈb ¹ˢᵗc ⁰ᵗʰa ⟩, a > b > c
6th|5th|4th|3rd|0th → 3
#125034_v2.0
WR 2023-10-05
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁵ᵗʰa ⁴ᵗʰb ³ʳᵈc ⟩, a > b > c
4th → a, 3rd → b, ab=1+5n
5th → a, 2nd → b, |a-b|=5
⟨⋯ Perm(0,1) ⋯⟩
#125034_v2.0
Q1(m=6) 2023-10-03
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦5,6⟧ ∋ 4
4th → a, 1st → b, |a-b|=2
6th → a, 5th → b, a+b=3
⟨⋯ 0 ⋯ a ⋯⟩, a = 1|3|5|6
⛔Avoid
⟨⋯ Perm(2,5) ⋯⟩
Sim⟨ ⁶ᵗʰ1 ⁵ᵗʰ6 ⁴ᵗʰ5 ³ʳᵈ0 ²ⁿᵈ2 ¹ˢᵗ4 ⁰ᵗʰ3 ⟩ = 2
Sim⟨ ⁶ᵗʰ2 ⁵ᵗʰ6 ⁴ᵗʰ4 ³ʳᵈ5 ²ⁿᵈ1 ¹ˢᵗ3 ⁰ᵗʰ0 ⟩ ≤ 1
#125034_v2.0
WR 2023-10-03
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → a, 1st → b, |a-b|=1
4th → a, 1st → b, ab=3+5n
⟨⋯ 5 ⋯ 1 ⋯ 2 ⋯⟩
⛔Avoid
4th|3rd → 1
5th|3rd|2nd|1st → 0
#125034_v2.0
Q1(m=6) 2023-10-01
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 5 ⋯ ? ⋯ 3 (?+6)⟩
⟨ ⁶ᵗʰc ⁵ᵗʰd ³ʳᵈa ¹ˢᵗb ⟩, a > b > c > d
3rd → a, 0th → b, a+b=3+4n
#125034_v2.0
WR 2023-10-01
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁴ᵗʰb ³ʳᵈc ²ⁿᵈa ⟩, a > b > c
⟨? ⋯ 4 ⋯ (?−2) ⋯⟩ (?≠4)
⟨⋯ 0 ⋯ a ⋯⟩, a = 1|3
⟨⋯ 5 ⋯ 2 ⋯ 0 ⋯⟩
⛔Avoid
⟨⋯ 0 ⋯ 4 ⋯⟩
#125034_v2.0
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