Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁶ᵗʰ↓ ⁵ᵗʰ↑ ²ⁿᵈ↓ ⟩ after 3×⟨←⟩
6th → a, 3rd → b, a+b=2+5n
0th → 0|3|6
Sim⟨ ⁶ᵗʰ1 ⁵ᵗʰ6 ⁴ᵗʰ5 ³ʳᵈ0 ²ⁿᵈ3 ¹ˢᵗ4 ⁰ᵗʰ2 ⟩ = 1
5th → 2
#125034_v2.2
Originating from a math proof, 125034 is a game driven by combinatorics, logic, and probability.
2023-12-31 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+5n
1st → 1|2|3|5
⛔Avoid
2nd → a, 1st → b, |a-b|=2
⟨? 2 ⋯ (?+1) ⋯ 5 ⋯⟩ (?≠2,1)
5th|3rd|2nd|0th → 2
⟨? 2 ⋯ (?−2) ⋯ 5 ⋯⟩ (?≠2,4)
⟨⋯ a ⋯ 3 ⋯⟩, a = 0|2|4
⟨⋯ 0 ⋯ 5 ⋯ 1 ⋯⟩
#125034_v2.2
2023-12-29 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ Perm(1,3,5) ⋯⟩
Jump(3,5) = 1
0 ∾ 1 ∾ 2 ∾ 3 ∾ 4 ∾ 5
⛔Avoid
Jump(2,4) ≥ 1
⟦0,2⟧ ∋ 4,5
#125034_v2.2
2023-12-28 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → a, 2nd → b, |a-b|=2
⟨⋯ Perm(1,5) ⋯⟩
5th → a, 0th → b, ab=12
⟨ ⁵ᵗʰ↑ ⁴ᵗʰ↓ ³ʳᵈ↓ ²ⁿᵈ↑ ¹ˢᵗ↑ ⁰ᵗʰ↓ ⟩ after ⟨⇌⟩
#125034_v2.2
2023-12-26 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
Sim⟨ ⁵ᵗʰ1 ⁴ᵗʰ3 ³ʳᵈ2 ²ⁿᵈ4 ¹ˢᵗ5 ⁰ᵗʰ0 ⟩ ≥ 1
4th → a, 2nd → b, ab=5
⟦0,3⟧ ∋ 4
⛔Avoid
1st|0th → 3
⟨⋯ Perm(0,4) ⋯⟩
⟨⋯ Perm(1,2,4) ⋯⟩
#125034_v2.2
2023-12-21 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → 1|2|5|6
⟨? ⋯ 1 ⋯ (?+2) ⋯⟩ (?≠1)
⟨⋯ ? ⋯ 6 ⋯ (?+4)⟩ (?≠2)
6th → a, 5th → b, a+b=5+6n
⟨⋯ ? ⋯ 6 ⋯ (?+3)⟩ (?≠3)
Jump(1,4) = 1
3rd → 1|2|6
⛔Avoid
⟨ ²ⁿᵈa ¹ˢᵗb ⟩, (ab)₁₀ ≥ 46
#125034_v2.2
2023-12-20 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦4,5⟧ ∋ 2,6
⟨⋯ Perm(0,3,4) ⋯⟩
2nd → a, 1st → b, a+b=7
4th → 3|4
⛔Avoid
⟨ ²ⁿᵈa ⁰ᵗʰb ⟩, (ab)₁₀ ≤ 60
5th → 0|1|3|5
#125034_v2.2
2023-12-19 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
6th → a, 0th → b, ab=0
3rd → a, 2nd → b, ab=0+6n
5th → a, 2nd → b, a+b=0+5n
⛔Avoid
⟨ ⁵ᵗʰb ⁴ᵗʰa ⟩, a > b
Sim⟨ ⁶ᵗʰ3 ⁵ᵗʰ5 ⁴ᵗʰ2 ³ʳᵈ6 ²ⁿᵈ0 ¹ˢᵗ1 ⁰ᵗʰ4 ⟩ ≥ 1
⟨⋯ 4 ⋯ 1 ⋯ 3 ⋯ 2 ⋯⟩
⟨⋯ 1 ⋯ ? ⋯ 5 (?−1)⟩ (?≠5,6)
⟨⋯ 2 ⋯ a ⋯⟩, a = 0|1|3|4|5
#125034_v2.2
2023-12-19 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
2nd → a, 0th → b, ab=0
Sim⟨ ⁵ᵗʰ2 ⁴ᵗʰ1 ³ʳᵈ0 ²ⁿᵈ5 ¹ˢᵗ3 ⁰ᵗʰ4 ⟩ = 2
5th → a, 0th → b, a+b=9
⟨⋯ 3 ⋯ 0 ⋯ 4 ⋯⟩
#125034_v2.2
2023-12-18 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
⟦1,5⟧ ∋ 2,3
⟨ ³ʳᵈa ⁰ᵗʰb ⟩, (ab)₁₀ ≥ 51
6th → a, 1st → b, a+b=1+4n
⛔Avoid
1st → 4
----- Information -----
🔲 「4th → a, 2nd → b, a+b=3」
480 permutations match this pattern.
Examples: ⟨0426135⟩, ⟨2135046⟩, ⟨6204351⟩.
🔲 「⟦1,5⟧ ∋ 2,3」
The closed interval given by 1 and 5 contains 2, 3.
840 permutations match this pattern.
Examples: ⟨0413256⟩, ⟨0532461⟩, ⟨1403625⟩.
🔲 「⟨ ³ʳᵈa ⁰ᵗʰb ⟩, (ab)₁₀ ≥ 51」
(ab)₁₀ ∶= 10a + b.
1320 permutations match this pattern.
Examples: ⟨3605241⟩, ⟨4016253⟩, ⟨0216354⟩.
🔲 「6th → a, 1st → b, a+b=1+4n」
[6th] + [1st] = 1 | 5 | 9 | ⋯ .
1440 permutations match this pattern.
Examples: ⟨5021643⟩, ⟨5601243⟩, ⟨6054231⟩.
🔳 「1st → 4」
720 permutations match this pattern.
Examples: ⟨1206345⟩, ⟨2306541⟩, ⟨6132045⟩.
#125034_v2.2
2023-12-17 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 0 ⋯ 2 ⋯ 3 ⋯⟩
⟦4,5⟧ ∋ 1
⟨⋯ 4 ⋯ 2 ⋯ 1 ⋯⟩
⟨⋯ ? ⋯ 6 ⋯ (?−1)⟩ (?≠6)
⛔Avoid
⟨ ⁶ᵗʰa ⁵ᵗʰb ⁴ᵗʰc ⟩, (abc)₁₀ ≤ 163
1st → a, 0th → b, a+b=8
#125034_v2.2
2023-12-17 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
4th|2nd|1st → 5
4th → a, 0th → b, ab=20
4th|2nd|1st → 3
⛔Avoid
2nd → 1|4|5
⟨⋯ ? ⋯ 2 ⋯ (?−1)⟩ (?≠2,3)
2nd → a, 0th → b, |a-b|=1
#125034_v2.2
2023-12-16 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁴ᵗʰa ¹ˢᵗb ⟩, (ab)₁₀ ≥ 52
⟨⋯ ? ⋯ 4 ⋯ (?+1)⟩ (?≠4,3)
⟨⋯ ? ⋯ 5 ⋯ (?−1)⟩ (?≠5,6)
6th → a, 2nd → b, a+b=6
⛔Avoid
6th|3rd|2nd|1st|0th → 1
#125034_v2.2
2023-12-15 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → 3
6th → a, 0th → b, ab=24
2nd → 0|5|6
3rd → a, 0th → b, a+b=0+6n
⛔Avoid
5th → a, 1st → b, a+b=8
⟦0,6⟧ ∋ 1,2,5
Jump(0,5) = 1
2nd → a, 1st → b, a+b=6
#125034_v2.2
2023-12-15 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 4 ⋯ 0 ⋯ 3 ⋯⟩
⟨? ⋯ 1 (?−1) ⋯ 3 ⋯⟩ (?≠1,2)
⛔Avoid
⟨⋯ a ⋯ 2 ⋯⟩, a = 0|1|4
#125034_v2.2
2023-12-14 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦2,6⟧ ∋ 1,3
⟨? ⋯ 0 (?−1) ⋯ 4 ⋯⟩ (?≠1)
⟨⋯ Perm(1,3,4) ⋯⟩
2nd → a, 1st → b, a+b=9
⛔Avoid
3rd → 0|2|4|6
#125034_v2.2
2023-12-14 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
4th → a, 2nd → b, |a-b|=1
⟨⋯ 5 ⋯ 4 ⋯ 0 ⋯⟩
1st → 0|1|3
⛔Avoid
⟨ ²ⁿᵈa ¹ˢᵗb ⟩, (ab)₁₀ ≤ 41
5th → 0|2|3
#125034_v2.2
2023-12-13 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
6th → a, 2nd → b, a+b=2
5th → a, 4th → b, a+b=7
1st → 3
⛔Avoid
Sim⟨ ⁶ᵗʰ6 ⁵ᵗʰ0 ⁴ᵗʰ2 ³ʳᵈ1 ²ⁿᵈ3 ¹ˢᵗ5 ⁰ᵗʰ4 ⟩ ≥ 1
Jump(2,5) = 1
6th|5th|2nd|1st|0th → 6
#125034_v2.2
2023-12-12 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 5 ⋯ ? ⋯ 6 (?−1)⟩ (?≠6)
⟨⋯ Perm(0,4,6) ⋯⟩
⟨? 3 ⋯ (?−4) ⋯ 2 ⋯⟩
⛔Avoid
4th|3rd|2nd → 2
⟨⋯ 4 ⋯ 0 ⋯ 6 ⋯⟩
#125034_v2.2
2023-12-12 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
5th → a, 3rd → b, ab=0
⟨⋯ ? ⋯ 1 ⋯ (?+5)⟩
4th → a, 2nd → b, a+b=2+4n
⛔Avoid
5th → 0|1|4
Jump(1,2) = 2
#125034_v2.2
2023-12-11 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
Jump(1,2) = 1
4th → 1
Jump(2,4) = 2
Jump(3,6) = 1
⛔Avoid
5th|4th|3rd|0th → 6
⟨ ⁵ᵗʰa ¹ˢᵗb ⟩, (ab)₁₀ ≥ 16
#125034_v2.2
2023-12-10 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)
Jump(4,5) = 2
⟨ ⁶ᵗʰa ¹ˢᵗb ⟩, (ab)₁₀ ≥ 13
6th|5th|4th|2nd|0th → 6
⛔Avoid
⟦2,4⟧ ∋ 1
5th → a, 2nd → b, a+b=2+4n
2nd → a, 1st → b, a+b=10
⟨? ⋯ 2 ⋯ (?−3) ⋯⟩ (?≠5)
#125034_v2.2
2023-12-10 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ²ⁿᵈa ¹ˢᵗb ⟩, a > b
⟨⋯ Perm(3,4,5) ⋯⟩
⛔Avoid
4th → a, 2nd → b, ab=0+4n
0 ∾ 1 ∾ 3
Sim⟨ ⁵ᵗʰ5 ⁴ᵗʰ1 ³ʳᵈ4 ²ⁿᵈ3 ¹ˢᵗ2 ⁰ᵗʰ0 ⟩ = 1
⟨⋯ 2 ⋯ a ⋯⟩, a = 0|1|4
⟨⋯ 4 ⋯ 1 ⋯⟩
#125034_v2.2
2023-12-09 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, a+b=5
⟨? ⋯ 3 ⋯ (?+2) ⋯⟩ (?≠3,1)
⟨ ⁶ᵗʰa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≥ 210
⛔Avoid
Jump(0,3) = 0
⟨⋯ 1 ⋯ a ⋯⟩, a = 3|4|6
0th → 0|1|4|6
#125034_v2.2
2023-12-08 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
2nd → a, 0th → b, a+b=3
⟨ ⁶ᵗʰa ⁵ᵗʰd ⁴ᵗʰb ³ʳᵈc ⟩, a > b > c > d
⟨ ⁴ᵗʰa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≥ 531
⟨⋯ Perm(4,5) ⋯⟩
⛔Avoid
1 ∾ 2 ∾ 5
#125034_v2.2
2023-12-08 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → 1|3|4
1st → a, 0th → b, |a-b|=4
⛔Avoid
⟨⋯ a ⋯ 1 ⋯⟩, a = 0|2|5
5th|4th|2nd|0th → 4
⟨ ⁴ᵗʰ↑ ¹ˢᵗ↓ ⟩ after 3×⟨←⟩
#125034_v2.2
2023-12-07 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ Perm(1,4) ⋯⟩
⟨⋯ 5 ⋯ 6 ⋯⟩
⟦0,4⟧ ∋ 5,6
1st → 0
⟨? ⋯ 3 (?+1) ⋯ 5 ⋯⟩ (?≠3,2)
#125034_v2.2
2023-12-07 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ Perm(0,3,5) ⋯⟩
⟨ ⁵ᵗʰb ⁴ᵗʰc ³ʳᵈa ⟩, a > b > c
2nd → a, 0th → b, a+b=5
⛔Avoid
⟦1,3⟧ ∋ 0,5
⟨⋯ 4 ⋯ 0 ⋯ 3 ⋯⟩
2nd → 3
#125034_v2.2
2023-12-05 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁴ᵗʰa ³ʳᵈb ⁰ᵗʰc ⟩, a > b > c
⟨? ⋯ 1 (?+2) ⋯ 4 ⋯⟩ (?≠1)
⟨ ⁶ᵗʰ↓ ⁵ᵗʰ↑ ³ʳᵈ↑ ⟩ after ⟨→⟩
⛔Avoid
Jump(2,6) ≥ 1
⟨⋯ 2 ⋯ 6 ⋯⟩
6th|4th|2nd → 0
#125034_v2.2
2023-12-05 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
3rd → a, 0th → b, |a-b|=1
Jump(0,3) = 0
⟨⋯ 4 ⋯ 5 ⋯⟩
Jump(2,5) = 0
⟦0,2⟧ ∋ 1,5
⛔Avoid
⟨ ⁴ᵗʰc ¹ˢᵗa ⁰ᵗʰb ⟩, a > b > c
#125034_v2.2
2023-12-04 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ ? ⋯ 2 ⋯ (?+2)⟩ (?≠2,0)
⟨⋯ Perm(1,5) ⋯⟩
4th → a, 0th → b, a+b=1+5n
⛔Avoid
⟨⋯ Perm(2,6) ⋯⟩
5th → a, 3rd → b, ab=0+5n
3rd → 1|2|4|5
⟨⋯ Perm(2,3,5) ⋯⟩
4th → a, 1st → b, a+b=1+6n
#125034_v2.2
2023-12-03 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨⋯ 1 ⋯ 2 ⋯ 3 ⋯⟩
Jump(2,4) ≥ 1
⟨⋯ 3 ⋯ a ⋯⟩, a = 0|1|2|6
5th → a, 2nd → b, a+b=2+5n
Jump(0,5) = 0
⛔Avoid
⟨⋯ a ⋯ 2 ⋯⟩, a = 0|4|6
4th → 3
⟦0,1⟧ ∋ 2,3,5,6
#125034_v2.2
2023-12-03 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟦3,4⟧ ∋ 2,5
⟨⋯ 0 ⋯ ? 5 ⋯ (?+1)⟩ (?≠4)
4th → a, 2nd → b, a+b=5
5th|4th|3rd → 2
#125034_v2.2
2023-12-01 Q1(m=6)
Rearrange the digits in ⟨1263045⟩ to meet the rules below.
⟨6th 5th 4th 3rd 2nd 1st 0th⟩
✅Match
⟨ ⁶ᵗʰb ⁵ᵗʰa ⁴ᵗʰd ³ʳᵈc ⟩, a > b > c > d
⛔Avoid
4th → a, 3rd → b, |a-b|=1
⟨⋯ a ⋯ 1 ⋯⟩, a = 0|2|6
Jump(3,6) ≥ 1
Jump(2,3) = 1
#125034_v2.2
2023-12-01 WR
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨5th 4th 3rd 2nd 1st 0th⟩
✅Match
2nd → a, 0th → b, ab=10
Jump(1,4) ≤ 1
3rd → 0|1|2
⛔Avoid
⟨⋯ ? ⋯ 3 ⋯ (?+1)⟩ (?≠3,2)
⟨⋯ 0 ⋯ ? 1 ⋯ (?+2)⟩ (?≠1)
3rd|2nd → 5
⟨? ⋯ 4 (?−2) ⋯ 0 ⋯⟩ (?≠4)
#125034_v2.2
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