2026-09-18 Q42(v=0) Rearrange the digits in 〈125034〉 to meet the rules below. 〈 ⁵▨ ⁴▨ ³▨ ²▨ ¹▨ ⁰▨ 〉 ■ Match: 5th → a, 2nd → b, ab=12 〈⋯ ⁿa ⋯〉, n+a=8+2k ● Avoid: 〈⋯ ⁿa ⋯〉, n+a=1+5k 〈⋯ ⁿa ⋯〉, na=2+10k https://125034.blogspot.com/2026/09/2026-09-18-q42v0.html #125034_v2.15

2026-07-28 M43 P1 ■ Match: 5th|4th|2nd → 1 〈? 0 ⋯ (?−1) ⋯ 3 ⋯〉 (?≠1) [[2,3]] ∋ 1 5th|4th|2nd|0th → 5 ● Avoid: 〈⋯ ? ⋯ 5 ⋯ (?−2)〉 (?≠5) [[3,5]] ∋ 0,4 〈403125〉 〈402135〉 Last HP: 1 P1 defeated P2! #125034_v2.14

2026-04-18 Q3 Rearrange the digits in 〈125034〉 to meet the rules below. 〈 ⁵▨ ⁴▨ ³▨ ²▨ ¹▨ ⁰▨ 〉 ■ Match: 5th → a, 1st → b, ab=0+5n 〈⋯ 4 ⋯ 2 ⋯ 1 ⋯〉 ● Avoid: min {p5, p4, p2} = 0 〈⋯ ⁿa ⋯〉, n+a=3 〈⋯ ⁿa ⋯〉, |n-a|=1 https://125034.blogspot.com/2026/04/2026-04-18-q3.html #125034_v2.13

2026-01-31 D 2P ■ Match: 〈⋯ a ⋯ 0 ⋯〉, a = 3|5 Jump(3,5) ≤ 2 〈⋯ 0 ⋯ 4 ⋯ 3 ⋯〉 2nd → a, 0th → b, a+b=3+4n ● Avoid: 〈⋯ 5 ⋯ 2 ⋯ 4 ⋯〉 〈 ⁴a ²b ⁰c 〉, (abc)₁₀ ≥ 305 〈 ⁵a ²b ⁰c 〉, (abc)₁₀ ≤ 105 max ⊢0⊣ = 3 Last HP: 0 1P defeated 2P! #125034_v2.12

2025-11-14 Q2(v=1) Rearrange the digits in 〈125034〉 to meet the rules below. 〈 ⁵▨ ⁴▨ ³▨ ²▨ ¹▨ ⁰▨ 〉 ■ Match: [[1,2]] ∋ 3,4 [[0,3]] ∋ 4,5 [[2,4]] ∋ 5 ● Avoid: 〈⋯ ⁿa ⋯〉, |n-a|=0 〈⋯ ⁿa ⋯〉, |n-a|=5 〈⋯ ⁿa ⋯〉, |n-a|=4 https://125034.blogspot.com/2025/11/2025-11-14-q2v1.html #125034_v2.11

2025-08-12 WR Rearrange the digits in 〈125034〉 to meet the rules below. 〈5th 4th 3rd 2nd 1st 0th〉 ■ Match: 〈? ⋯ 5 (?+1) ⋯ 0 ⋯〉 (?≠4) ● Avoid: 〈 ⁵a ²b ⁰c 〉, a > b > c 〈⋯ a ⋯ 5 ⋯〉, a = 0|1|2|4 [1,4] ∋ 0 ************************************** ５４３２１０ －－－－－－ －５－－－－ ３５－－－－ ３５４－－－ ３５４－－２ ３５４１－２ ３５４１０２ https://125034.blogspot.com/2025/08/2025-08-12-wr.html #125034_v2.10

2025-04-29 Q1 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▧ ≥ ▢ 〈 ⁵a ³b ²c 〉, (abc)₁₀ ≤ 310 ************************************** 5 4 3 2 1 0 ‒ ‒ ‒ ‒ ‒ ‒ 3 ‒ ‒ ‒ ‒ ‒ 3 ‒ ‒ ‒ ‒ 5 3 ‒ ‒ 0 ‒ 5 3 ‒ 4 0 ‒ 5 3 1 4 0 ‒ 5 3 1 4 0 2 5 https://125034.blogspot.com/2025/04/2025-04-29-q1.html #125034_v2.9

2024-12-11 WR Rearrange the digits in 〈125034〉 to meet the rules below. 〈5th 4th 3rd 2nd 1st 0th〉 ■ Match: {p4, p3, p1} = ? + {0,1,2} min {p4, p3} = 0 ● Avoid: 〈 ⁴a ⁰b 〉, (ab)₁₀ ≤ 15 〈⋯ 3 ⋯ 1 ⋯ 4 ⋯〉 〈⋯ 0 ⋯ 3 ⋯〉 #125034_v2.8 Answer: https://125034.blogspot.com/2024/12/2024-12-11-wr.html

2024-10-11 Q3 Rearrange the digits in 〈125034〉 to meet the rules below. 〈5th 4th 3rd 2nd 1st 0th〉 ■ Match: median {p5, p4, p0} = 2 {p4, p3, p2} = ? + {0,2,3} Sim〈352410〉 ≥ 2 ● Avoid: min ⊢4⊣ = 1 max {p5, p2, p1} = 5 #125034_v2.7 Answer: https://125034.blogspot.com/2024/10/2024-10-11-q3.html

2024-07-26 WR Rearrange the digits in 〈125034〉 to meet the rules below. 〈5th 4th 3rd 2nd 1st 0th〉 Match: 1st → 1|5 〈 ⁴↑ ³↑ 〉 after 2×〈←〉 5th → a, 2nd → b, a+b=0+4n 〈⋯ 4 ⋯ a ⋯〉, a = 1|2|5 {p5, p3, p0} = ? + {0,1,2} Avoid: 〈 ⁵a ²b ¹c 〉, (abc)₁₀ ≤ 231 #125034_v2.6 Answer: https://125034.blogspot.com/2024/07/2024-07-26-wr.html

2024-05-02 M3 P2 (老羅) Match: max ⊢1⊣ ≤ 3 4th → a, 0th → b, a+b=5 〈⋯ Perm(0,1,3) ⋯〉 {p5, p2, p1} = ? + {0,1,2} Avoid: Sim〈 ⁵2 ⁴4 ³0 ²3 ¹5 ⁰1 〉 ≥ 1 Last HP: 0 Lowe the Lion defeated 老羅! #125034_v2.5 (Answer: https://125034.blogspot.com/2024/05/2024-05-02-m3.html)

2024-03-11 M4 P2 (Ryan) Match: 5th|1st → 2 5th → a, 2nd → b, |a-b|=5 〈 ⁵a ²b 〉, (ab)₁₀ ≤ 32 〈 ³a ⁰b 〉, a > b 〈⋯ ? ⋯ 3 ⋯ (?+1)〉 (?≠3,2) Avoid: min ⊢5⊣ = 1 max ⊢3⊣ = 3 〈⋯ ? ⋯ 0 ⋯ (?−1)〉 (?≠1) 〈043521〉 Last HP: 0 Ryan gave you the same finish! #125034_v2.4

2024-01-25 Q1(m=6) Rearrange the digits in 〈1263045〉 to meet the rules below. 〈6th 5th 4th 3rd 2nd 1st 0th〉 ▲ Match: 〈 ³a ¹b 〉, min[[a,b]] = 1 [[4,6]] ∋ 1,2,3,5 〈⋯ Perm(2,5) ⋯〉 〈⋯ 6 ⋯ ? 3 ⋯ (?−1)〉 (?≠3,4) ▼ Avoid: 5th|2nd|0th → 0 ----- Information ----- ● 「〈 ³a ¹b 〉, min[[a,b]] = 1」 The least element of { [3rd], [2nd], [1st] } is 1. 1440 permutations match this pattern. Examples: 〈3052614〉, 〈4526130〉, 〈4621530〉. ● 「[[4,6]] ∋ 1,2,3,5」 The closed interval given by 4 and 6 contains 1, 2, 3, 5. 336 permutations match this pattern. Examples: 〈6105324〉, 〈4310526〉, 〈4503216〉. ● 「〈⋯ Perm(2,5) ⋯〉」 2,5 are adjacent. 1440 permutations match this pattern. Examples: 〈6302541〉, 〈1520364〉, 〈4032516〉. ● 「〈⋯ 6 ⋯ ? 3 ⋯ (?−1)〉 (?≠3,4)」 ?, 3, (?−1) are three different numbers. 300 permutations match this pattern. Examples: 〈2631405〉, 〈4206315〉, 〈6153024〉. ● 「5th|2nd|0th → 0」 2160 permutations match this pattern. Examples: 〈4365012〉, 〈1042563〉, 〈1356420〉. ************** Riddle Analysis －－－－－－－ (M)「[[4,6]] ∋ 1,2,3,5」 (M)「〈⋯ 6 ⋯ ? 3 ⋯ (?−1)〉 (?≠3,4)」 (A)「5th|2nd|0th → 0」 －－－－－－４ (M)「〈 ³a ¹b 〉, min[[a,b]] = 1」 (M)「〈⋯ Perm(2,5) ⋯〉」 (M)「〈⋯ 6 ⋯ ? 3 ⋯ (?−1)〉 (?≠3,4)」 －－２５３１４ (A)「5th|2nd|0th → 0」 ０６２５３１４ #125034_v2.3

2023-11-22 WR Rearrange the digits in 〈125034〉 to meet the rules below. 〈5th 4th 3rd 2nd 1st 0th〉 Match: 〈⋯ Perm(3,4,5) ⋯〉 [1,4] ∋ 0,3 3rd → a, 0th → b, ab=0 Jump(2,4) = 2 ----- Information ----- ● 「〈⋯ Perm(3,4,5) ⋯〉」 3,4,5 are adjacent. 144 permutations match this pattern. Examples: 〈120543〉, 〈243510〉, 〈201345〉. ● 「[1,4] ∋ 0,3」 The closed interval given by 1 and 4 contains 0, 3. 120 permutations match this pattern. Examples: 〈420531〉, 〈132504〉, 〈103245〉. ● 「3rd → a, 0th → b, ab=0」 240 permutations match this pattern. Examples: 〈230451〉, 〈250143〉, 〈241350〉. ● 「Jump(2,4) = 2」 There are 2 numbers between 2 and 4. 144 permutations match this pattern. Examples: 〈345021〉, 〈403251〉, 〈134502〉. ************** ５４３２１０ －－－－－－ －－０－－－ －２０－－－ １２０－－－ １２０－４－ １２０３４－ １２０３４５ ************** Proof. https://125034.blogspot.com/2023/11/2023-11-22-wr.html Q.E.D. #125034_v2.2

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 ************** ６５４３２１０ －－－－－－－ －－－－－－２ ３－－－－－２ ３１－－－－２ ３１０－－－２ ３１０－－５２ ３１０－４５２ ３１０６４５２ Proof. https://125034.blogspot.com/2023/10/q1m6-2023-10-23.html Q.E.D. #125034_v2.1

Q21 1830-08-30 Rearrange the digits in 〈125034〉 to meet the rules below. 〈5th 4th 3rd 2nd 1st 0th〉 Match: [0,5] ∋ 1,4 〈 ³b ¹c ⁰a 〉, a > b > c Avoid: 〈⋯ Perm(2,5) ⋯〉 〈 ²a ⁰b 〉, (ab)₁₀ ≤ 23 〈⋯ 3 ⋯ 2 ⋯〉 〈⋯ 0 ⋯ 1 ⋯〉 #125034_v2.0 ************** ５４３２１０ －－－－－－ －－－－０－ ５－－－０－ ５－－－０３ ５－２－０３ ５－２４０３ ５１２４０３

WR 1864-07-24 Rearrange the digits in 〈125034〉 to meet the rules below. 〈5th 4th 3rd 2nd 1st 0th〉 Match: 5th → 1|2|3|5 4th → a, 1st → b, a+b=5 〈 ⁴a ²b ¹c 〉, (abc)₁₀ ≥ 210 〈⋯ Perm(1,2) ⋯〉 〈 ⁵a ²b 〉, (ab)₁₀ ≤ 25 Avoid: 〈 ³a ²b ¹c 〉, (abc)₁₀ ≥ 302 3rd → a, 2nd → b, a+b=4 #125034_v1.7 ************** ５４３２１０ －－－－－－ １－－－－－ １２－－－－ １２－－３－ １２０－３－ １２０５３－ １２０５３４

Performance improvements

WR 1816-04-22 Rearrange the digits in 〈125034〉 to meet the rules below. 〈5th 4th 3rd 2nd 1st 0th〉 Match: 〈⋯ 5 ⋯ 1 ⋯ 4 ⋯〉 [0,4] ∋ 2,5 1 ∾ 4 ∾ 5 Avoid: Jump(1,2) = 0 #125034_v1.5 ****** ５４３２１０ －－－－－－ ０－－－－－ ０－－１－－ ０２－１－－ ０２５１－－ ０２５１－４ ０２５１３４

Lowe the Lion's riddle Rearrange the digits in 〈125034〉 to meet the rules below. 〈5th 4th 3rd 2nd 1st 0th〉 Match: 〈 5th↑ 4th↓ 3rd↓ 2nd↓ 1st↑ 0th↑ 〉 after 5−〈⋯〉 5th → a, 2nd → b, ab=10 Avoid: 2nd → a, 0th → b, a+b=5 〈⋯ Perm(0,4,5) ⋯〉 #125034 v1.4

M1 1713-11-07 P2 (Matthew) Match: 〈⋯ 4 ⋯ 5 ⋯ 3 ⋯〉 3rd → a, 2nd → b, a+b=3+4n Avoid: 2nd → a, 1st → b, ab=20 [0,3] ∋ 4,5 1st → 1|2|4 Jump(4,5) = 0 0th → 0|2|3 〈405231〉 Last HP: 0 Matthew gave you the same finish! #125034 v1.3

Q2(m=6) 1713-11-07 Rearrange the digits in 〈1263045〉 to meet the rules below. 〈6th 5th 4th 3rd 2nd 1st 0th〉 Match: 〈⋯ 4 ⋯ 2 ⋯ 0 ⋯ 5 ⋯〉 〈 6th↓ 5th= 4th↑ 3rd↓ 2nd↑ 1st↑ 0th↓ 〉 after 6−〈⋯〉 Avoid: 〈? ⋯ 3 ⋯ (?−1) ⋯〉 (?≠3,4) 6th → a, 4th → b, |a-b|=2 #125034 v1.2 - 1 - - - - - 1 1 - - - - - 1 1 - - - - 1 1 1 - 1 - - 1 1 1 - 1 1 - 1 1 1 - 1 1 1 1 1 1 1 1 1 1 1

M10 1713-11-07 P2 (? ? ?) Match: 5th|4th|2nd|0th → 3 〈⋯ Perm(2,3,5) ⋯〉 3rd → a, 2nd → b, a+b=2+5n Avoid: 〈⋯ Perm(2,5) ⋯〉 〈⋯ 0 ⋯ 2 ⋯ 4 ⋯〉 〈⋯ Perm(0,1,5) ⋯〉 〈532014〉 Last HP: 1 ? ? ? defeated you! #125034 v1.1