Blog of 125034: January 2026

2025-07-11 Q1-4(v=0)

2025-07-11 Q1

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨⋯ 5 ⋯ a ⋯⟩, a = 2|3|4

⛔Avoid

⟨⋯ a ⋯ 4 ⋯⟩, a = 1|2|5

⟨⋯ 0 ⋯ a ⋯⟩, a = 1|2|3|5

⟨⋯ a ⋯ 2 ⋯⟩, a = 1|5

⟨⋯ 1 ⋯ a ⋯⟩, a = 2|3|4

2025-07-11 Q2

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

max {p4, p3, p0} = 3

median {p5, p2, p0} = 2

max {p4, p2, p0} = 3

min {p5, p2, p1} = 2

⛔Avoid

min {p4, p1, p0} = 1

max {p5, p4, p2} = 4

2025-07-11 Q3

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

5th → a, 4th → b, a+b=3+5n

5th → a, 3rd → b, a+b=1+5n

3rd → a, 2nd → b, ab=2+5n

⛔Avoid

5th → a, 0th → b, ab=0+4n

2025-07-11 Q4

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

Sim⟨ ⁵ᵗʰ0 ⁴ᵗʰ1 ³ʳᵈ3 ²ⁿᵈ5 ¹ˢᵗ2 ⁰ᵗʰ4 ⟩ ≥ 2

Sim⟨ ⁵ᵗʰ0 ⁴ᵗʰ3 ³ʳᵈ1 ²ⁿᵈ4 ¹ˢᵗ2 ⁰ᵗʰ5 ⟩ ≤ 1

Sim⟨ ⁵ᵗʰ0 ⁴ᵗʰ2 ³ʳᵈ4 ²ⁿᵈ3 ¹ˢᵗ1 ⁰ᵗʰ5 ⟩ = 1

⛔Avoid

Sim⟨ ⁵ᵗʰ3 ⁴ᵗʰ0 ³ʳᵈ4 ²ⁿᵈ5 ¹ˢᵗ2 ⁰ᵗʰ1 ⟩ ≤ 1

Sim⟨ ⁵ᵗʰ0 ⁴ᵗʰ5 ³ʳᵈ2 ²ⁿᵈ1 ¹ˢᵗ4 ⁰ᵗʰ3 ⟩ ≤ 1

#125034_v2.11

https://puzzling.stackexchange.com/questions/135116/125034-v2-11-2025-07-11-q1-4v-0

The Ruritanian prime minister is in a fix. Thanks to a series of incompetent policy decisions, all five of her senior ministers need to be axed from their posts. However, the PM cannot afford to sack them completely, because they will wreak havoc if moved to the back benches.

She has a solution: a reshuffle! She will move each of the five ministers to one of the other top posts, but no two of them will directly swap with each other.

Anerdine will move to the department of the person who will become chancellor.
Brinkman will replace the person who will be the new home secretary.
Crass will take over the post being vacated by the person who will take Eejit’s job.
Dyer will be become health secretary even though he has been vying to be a chancellor, a post that he has never held.
The current defence secretary will get the department of the person who is becoming the education secretary.

Can you figure out who currently has which job, and where they are moving to?

Note: Nobody gets reassigned to their previous role.

https://puzzling.stackexchange.com/a/135112

https://puzzling.stackexchange.com/a/135115

2025-12-01 Ex1

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match
g(0) = 4
g(1) = 7
g(2) = 12
g(3) = 8
g(4) = 3
g(5) = 5

----- Information -----

Your goal is to find a permutation that satisfies every required pattern ✅ simultaneously.

There are 6 positions labeled 5th down to 0th, arranged left to right in descending order (5th is leftmost, 0th is rightmost). Therefore, ⟨125034⟩ = ⟨ ⁵ᵗʰ1 ⁴ᵗʰ2 ³ʳᵈ5 ²ⁿᵈ0 ¹ˢᵗ3 ⁰ᵗʰ4 ⟩.

It is given that

[5th] is connected to [2nd]
[4th] is connected to [3rd] and [2nd]
[3rd] is connected to [4th], [1st] and [0th]
[2nd] is connected to [5th], [4th] and [1st]
[1st] is connected to [3rd], [2nd] and [0th]
[0th] is connected to [3rd] and [1st]

By "g(X) = Y" we mean that the circles connected to X have numbers which sum to Y.

----- Required patterns -----

✅ 「g(0) = 4」
There are 48 permutations matching this pattern.
Examples: ⟨023415⟩, ⟨241530⟩, ⟨203154⟩, ⟨251430⟩.

✅ 「g(1) = 7」
There are 120 permutations matching this pattern.
Examples: ⟨340215⟩, ⟨253104⟩, ⟨520314⟩, ⟨204153⟩.

✅ 「g(2) = 12」
There are 36 permutations matching this pattern.
Examples: ⟨013524⟩, ⟨013425⟩, ⟨540231⟩, ⟨132054⟩.

✅ 「g(3) = 8」
There are 36 permutations matching this pattern.
Examples: ⟨510324⟩, ⟨023415⟩, ⟨053412⟩, ⟨405231⟩.

✅ 「g(4) = 3」
There are 108 permutations matching this pattern.
Examples: ⟨514320⟩, ⟨352041⟩, ⟨314520⟩, ⟨351024⟩.

✅ 「g(5) = 5」
There are 120 permutations matching this pattern.
Examples: ⟨254103⟩, ⟨402513⟩, ⟨234051⟩, ⟨204531⟩.

https://puzzling.stackexchange.com/a/135111

2026-01-31 D

✅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 ⋯⟩

⟨ ⁴ᵗʰa ²ⁿᵈb ⁰ᵗʰc ⟩, (abc)₁₀ ≥ 305

⟨ ⁵ᵗʰa ²ⁿᵈb ⁰ᵗʰc ⟩, (abc)₁₀ ≤ 105

max ⊢0⊣ = 3

Last HP: 0

1P defeated 2P!

#125034_v2.12

2026-01-30 Q1(m=6,v=0)

Rearrange the digits in ⟨1263045⟩ to meet the rules below.

⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

3rd → a, 2nd → b, |a-b|=3

⟨⋯ ᵃb ⋯⟩, |a-b|=4

⟨ ⁶ᵗʰ↓ ⁵ᵗʰ↓ ⁴ᵗʰ↑ ³ʳᵈ↓ ²ⁿᵈ= ¹ˢᵗ↑ ⁰ᵗʰ↑ ⟩ after 6−⟨⋯⟩

⛔Avoid

⟨⋯ ᵃb ⋯⟩, |a-b|=0

#125034_v2.11

2026-01-30 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

Sim⟨ ⁵ᵗʰ3 ⁴ᵗʰ2 ³ʳᵈ4 ²ⁿᵈ1 ¹ˢᵗ0 ⁰ᵗʰ5 ⟩ = 0

3rd → a, 1st → b, ab=3+5n

⛔Avoid

{p5, p3, p2} = ? + {0,1,2}

Sim⟨ ⁵ᵗʰ0 ⁴ᵗʰ1 ³ʳᵈ5 ²ⁿᵈ3 ¹ˢᵗ4 ⁰ᵗʰ2 ⟩ ≥ 1

4th → 0|3|4

⟨ ²ⁿᵈ↓ ¹ˢᵗ↓ ⟩ after 2×⟨←⟩

⟨ ²ⁿᵈa ⁰ᵗʰb ⟩, max⟦a,b⟧ = 3

#125034_v2.11

2026-01-29 Q1(m=6)

Rearrange the digits in ⟨1263045⟩ to meet the rules below.

⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

Jump(0,3) = 3

⟦1,5⟧ ∋ 3

⟨⋯ Perm(1,2) ⋯⟩

6th → a, 0th → b, a+b=0+4n

⛔Avoid

5th → 2|3|5

⟨⋯ Perm(2,6) ⋯⟩

#125034_v2.11

2026-01-29 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

4th → a, 1st → b, a+b=0+5n

min ⊢5⊣ ≥ 2

⟨? ⋯ 5 ⋯ (?+1) ⋯⟩ (?≠4)

⛔Avoid

Sim⟨ ⁵ᵗʰ5 ⁴ᵗʰ0 ³ʳᵈ3 ²ⁿᵈ4 ¹ˢᵗ2 ⁰ᵗʰ1 ⟩ = 0

⟦1,5⟧ ∋ 2,4

5th → a, 1st → b, |a-b|=2

min {p5, p3, p2} = 1

Jump(3,4) = 1

#125034_v2.11

2026-01-27 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

4th → a, 3rd → b, a+b=0+5n

⟨ ³ʳᵈb ²ⁿᵈa ¹ˢᵗc ⟩, a > b > c

5th → a, 2nd → b, a+b=0+5n

⟨ ³ʳᵈa ²ⁿᵈb ⁰ᵗʰc ⟩, (abc)₁₀ ≥ 150

⟨ ¹ˢᵗa ⁰ᵗʰb ⟩, (ab)₁₀ ≤ 21

⛔Avoid

⟨⋯ Perm(1,2,3) ⋯⟩

⟨⋯ 3 ⋯ 2 ⋯⟩

#125034_v2.11

2026-01-27 Q1(m=6)

Rearrange the digits in ⟨1263045⟩ to meet the rules below.

⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

median {p5, p2, p1} = 1

6th → 0|2|4|6

4th → a, 1st → b, a+b=6

2nd → 2|3|4

⛔Avoid

min {p6, p2, p1} = 1

⟨ ⁰ᵗʰ↓ ⟩ after 2×⟨→⟩

⟨? ⋯ 0 ⋯ (?−2) ⋯⟩ (?≠2)

#125034_v2.11

2026-01-25 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

{p5, p2, p0} = ? + {0,1,3}

⟨⋯ Perm(0,1,5) ⋯⟩

3rd → a, 1st → b, |a-b|=3

⛔Avoid

4th → 1|2|5

⟨? ⋯ 1 ⋯ (?−3) ⋯⟩ (?≠4)

⟨⋯ Perm(0,2) ⋯⟩

#125034_v2.11

2026-01-23 Q1(m=6,v=0)

Rearrange the digits in ⟨1263045⟩ to meet the rules below.

⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨ ⁵ᵗʰb ⁴ᵗʰa ¹ˢᵗc ⟩, a > b > c

⟨ ⁶ᵗʰa ⁵ᵗʰb ³ʳᵈc ⁰ᵗʰd ⟩, a > b > c > d

⟨ ⁴ᵗʰa ²ⁿᵈd ¹ˢᵗc ⁰ᵗʰb ⟩, a > b > c > d

⛔Avoid

⟨ ⁶ᵗʰb ⁴ᵗʰa ⁰ᵗʰc ⟩, a > b > c

#125034_v2.11

2026-01-23 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

1st → a, 0th → b, |a-b|=4

⟨⋯ 2 ⋯ ? ⋯ 5 (?−3)⟩ (?≠5)

{p5, p4, p1} = ? + {0,2,3}

⛔Avoid

4th → a, 3rd → b, ab=0

#125034_v2.11

2026-01-22 Q1(m=6)

Rearrange the digits in ⟨1263045⟩ to meet the rules below.

⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨⋯ a ⋯ 5 ⋯⟩, a = 0|2|3

⟨ ⁵ᵗʰc ³ʳᵈd ¹ˢᵗb ⁰ᵗʰa ⟩, a > b > c > d

⟨ ⁶ᵗʰa ²ⁿᵈb ⟩, max⟦a,b⟧ = 5

{p5, p4, p2} = ? + {0,1,3}

⛔Avoid

Jump(0,6) ≤ 2

Jump(2,4) ≥ 2

#125034_v2.11

2026-01-22 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟦2,4⟧ ∋ 0

⛔Avoid

Sim⟨ ⁵ᵗʰ2 ⁴ᵗʰ5 ³ʳᵈ0 ²ⁿᵈ4 ¹ˢᵗ1 ⁰ᵗʰ3 ⟩ ≥ 1

⟨⋯ ᵃb ⋯⟩, |a-b|=0

⟨ ⁴ᵗʰa ¹ˢᵗb ⟩, max⟦a,b⟧ = 5

min ⊢1⊣ = 1

⟨ − ▧ ▧ − ▢ − ⟩, Σ▧ ≤ ▢

#125034_v2.11

2026-01-20 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨⋯ Perm(0,1,5) ⋯⟩

min ⊢4⊣ ≤ 2

⛔Avoid

Jump(0,2) ≤ 2

⟦0,3⟧ ∋ 1,5

⟨⋯ 0 ⋯ a ⋯⟩, a = 3|4|5

#125034_v2.11

2026-01-20 Q1(m=6)

Rearrange the digits in ⟨1263045⟩ to meet the rules below.

⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨ ⁴ᵗʰa ²ⁿᵈb ¹ˢᵗc ⟩, (abc)₁₀ ≥ 540

median {p5, p2, p1} = 4

⟦0,6⟧ ∋ 2,4,5

2nd → 0|3|4

⛔Avoid

⟨⋯ a ⋯ 0 ⋯⟩, a = 1|2|3|5|6

1st → a, 0th → b, a+b=3+4n

6th → a, 5th → b, a+b=2

#125034_v2.11

2026-01-18 Q1(m=6,v=1)

Rearrange the digits in ⟨1263045⟩ to meet the rules below.

⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

4th → a, 0th → b, |a-b|=5

min ⊢4⊣ = 2

2nd → a, 1st → b, |a-b|=1

5th → a, 4th → b, |a-b|=1

min ⊢3⊣ ≤ 1

⛔Avoid

3rd → a, 1st → b, |a-b|=1

#125034_v2.11

2026-01-18 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨ ⁵ᵗʰb ³ʳᵈa ²ⁿᵈc ⟩, a > b > c

⟨? ⋯ 1 ⋯ (?−1) ⋯⟩ (?≠1,2)

⛔Avoid

⟨⋯ 0 ⋯ 2 ⋯⟩

⟨⋯ ᵃb ⋯⟩, |a-b|=0

#125034_v2.11

2026-01-16 Q1(m=6)

Rearrange the digits in ⟨1263045⟩ to meet the rules below.

⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨ ⁰ᵗʰ↓ ⟩ after ⟨←⟩

max ⊢0⊣ = 2

{p6, p4, p3} = ? + {0,1,3}

⟦0,6⟧ ∋ 3,4,5

⛔Avoid

5th → a, 4th → b, ab=0+6n

Sim⟨ ⁶ᵗʰ0 ⁵ᵗʰ3 ⁴ᵗʰ2 ³ʳᵈ6 ²ⁿᵈ4 ¹ˢᵗ5 ⁰ᵗʰ1 ⟩ = 1

#125034_v2.11

2026-01-16 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨ ⁵ᵗʰa ²ⁿᵈb ¹ˢᵗc ⟩, a > b > c

{p3, p2, p0} = ? + {0,1,2}

⟨⋯ ᵃb ⋯⟩, |a-b|=2

⛔Avoid

⟨ ⁴ᵗʰa ⁰ᵗʰb ⟩, a > b

⟨⋯ Perm(0,3,4) ⋯⟩

#125034_v2.11

2026-01-15 Q1(m=6)

Rearrange the digits in ⟨1263045⟩ to meet the rules below.

⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨⋯ ? ⋯ 6 ⋯ (?+5)⟩ (?≠1)

⟨⋯ Perm(4,5,6) ⋯⟩

⟨ ⁵ᵗʰa ⁴ᵗʰb ²ⁿᵈc ⟩, (abc)₁₀ ≤ 325

⛔Avoid

Sim⟨ ⁶ᵗʰ6 ⁵ᵗʰ3 ⁴ᵗʰ2 ³ʳᵈ4 ²ⁿᵈ0 ¹ˢᵗ5 ⁰ᵗʰ1 ⟩ ≤ 1

6th → a, 1st → b, ab=0+5n

#125034_v2.11

2026-01-15 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨ ³ʳᵈa ¹ˢᵗb ⟩, (ab)₁₀ ≤ 41

⟨ ⁴ᵗʰb ²ⁿᵈc ⁰ᵗʰa ⟩, a > b > c

Sim⟨ ⁵ᵗʰ2 ⁴ᵗʰ4 ³ʳᵈ5 ²ⁿᵈ1 ¹ˢᵗ3 ⁰ᵗʰ0 ⟩ ≥ 2

⛔Avoid

⟨⋯ ᵃb ⋯⟩, |a-b|=3

⟨⋯ a ⋯ 2 ⋯⟩, a = 0|3

#125034_v2.11

2026-01-13 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

max ⊢0⊣ ≥ 4

5th → a, 1st → b, a+b=9

⟨⋯ 5 ⋯ 4 ⋯⟩

⛔Avoid

⟨ − ▧ ▢ ▢ − − ⟩, ▧ ≤ Σ▢

4th → 1|3|4

#125034_v2.11

2026-01-13 Q1(m=6,v=1)

Rearrange the digits in ⟨1263045⟩ to meet the rules below.

⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

max ⊢3⊣ ≥ 4

{p6, p5, p3, p1} = ? + {0,1,2,3}

{p6, p5, p1, p0} = ? + {0,2,3,4}

{p5, p3, p1, p0} = ? + {0,1,3,4}

max ⊢0⊣ ≤ 3

⛔Avoid

min ⊢4⊣ ≥ 3

{p6, p5, p4, p3} = ? + {0,1,3,4}

#125034_v2.11

2026-01-11 Q1(m=6,v=0)

Rearrange the digits in ⟨1263045⟩ to meet the rules below.

⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

{p6, p4, p0} = ? + {0,1,2}

{p6, p1, p0} = ? + {0,2,4}

{p3, p2, p1, p0} = ? + {0,1,2,3}

{p6, p5, p4, p2} = ? + {0,2,3,4}

#125034_v2.11

2026-01-11 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨? ⋯ 1 ⋯ (?−2) ⋯⟩ (?≠3)

⟨⋯ 2 ⋯ 4 ⋯ 0 ⋯⟩

⟨ ⁴ᵗʰa ³ʳᵈb ⟩, (ab)₁₀ ≥ 43

4th → a, 1st → b, a+b=2+4n

⛔Avoid

{p5, p4, p3} = ? + {0,2,3}

#125034_v2.11

2026-01-09 Q1(m=6)

Rearrange the digits in ⟨1263045⟩ to meet the rules below.

⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨⋯ 1 ⋯ ? 3 ⋯ (?+1)⟩ (?≠3,2)

⛔Avoid

⟨⋯ Perm(1,3) ⋯⟩

⟨⋯ ᵃb ⋯⟩, |a-b|=3

6th|4th|3rd|0th → 4

3rd → a, 2nd → b, a+b=1+6n

3rd → a, 1st → b, |a-b|=5

⟨⋯ ᵃb ⋯⟩, |a-b|=4

⟨⋯ Perm(0,2,6) ⋯⟩

#125034_v2.11

2026-01-09 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

4th → 0|2|3

0 ∾ 2 ∾ 3 ∾ 4

{p5, p4, p2} = ? + {0,1,3}

⟨⋯ a ⋯ 0 ⋯⟩, a = 1|3|4|5

⛔Avoid

max {p5, p2, p0} = 5

⟨ ⁴ᵗʰa ²ⁿᵈb ⟩, max⟦a,b⟧ = 5

⟨⋯ ? ⋯ 1 ⋯ (?−2)⟩ (?≠3)

⟨⋯ Perm(3,4,5) ⋯⟩

#125034_v2.11

2026-01-08 Q1(m=6)

Rearrange the digits in ⟨1263045⟩ to meet the rules below.

⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨? 3 ⋯ (?+4) ⋯ 5 ⋯⟩

4th → a, 3rd → b, |a-b|=2

⟨? ⋯ 2 (?+1) ⋯ 1 ⋯⟩ (?≠2,1)

⛔Avoid

5th → a, 0th → b, ab=2+4n

⟨? ⋯ 6 ⋯ (?+1) ⋯⟩ (?≠5)

#125034_v2.11

2026-01-08 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨? 2 ⋯ (?−1) ⋯ 3 ⋯⟩ (?≠2,3)

3rd → 0

5th|4th|3rd|1st → 5

⛔Avoid

{p2, p1, p0} = ? + {0,2,3}

⟨ ²ⁿᵈa ⁰ᵗʰb ⟩, a > b

2nd → a, 1st → b, |a-b|=2

#125034_v2.11

2026-01-06 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨⋯ ᵃb ⋯⟩, |a-b|=0

⟨ ⁵ᵗʰa ²ⁿᵈb ⟩, max⟦a,b⟧ = 4

⟨⋯ Perm(1,2,4) ⋯⟩

⟨⋯ ᵃb ⋯⟩, |a-b|=2

⟦2,5⟧ ∋ 4

⛔Avoid

⟨? ⋯ 5 ⋯ (?−1) ⋯⟩ (?≠5)

⟨⋯ ? ⋯ 1 ⋯ (?+2)⟩ (?≠1)

⟨ − − ▧ ▧ − ▢ ⟩, Σ▧ ≤ ▢

{p4, p3, p2} = ? + {0,1,3}

#125034_v2.11

2026-01-06 Q1(v=0)

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

0 ∾ 1 ∾ 3

⟨ ²ⁿᵈ↓ ⟩ after 2×⟨←⟩

⛔Avoid

3 ∾ 5

1 ∾ 3 ∾ 4

0 ∾ 1 ∾ 2 ∾ 3

2 ∾ 5

2 ∾ 4

4 ∾ 5

#125034_v2.11

2026-01-04 Q1(m=6,v=1)

Rearrange the digits in ⟨1263045⟩ to meet the rules below.

⟨ ⁶ᵗʰ▨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

2 ∾ 3 ∾ 6

0 ∾ 1 ∾ 4

0 ∾ 4 ∾ 5

⛔Avoid

1 ∾ 2 ∾ 3 ∾ 4 ∾ 5 ∾ 6

Sim⟨ ⁶ᵗʰ6 ⁵ᵗʰ4 ⁴ᵗʰ2 ³ʳᵈ1 ²ⁿᵈ5 ¹ˢᵗ0 ⁰ᵗʰ3 ⟩ ≥ 1

Sim⟨ ⁶ᵗʰ2 ⁵ᵗʰ6 ⁴ᵗʰ0 ³ʳᵈ1 ²ⁿᵈ3 ¹ˢᵗ4 ⁰ᵗʰ5 ⟩ ≥ 1

#125034_v2.11

2026-01-04 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨⋯ 0 ⋯ a ⋯⟩, a = 1|2|4

⟨⋯ Perm(2,3,5) ⋯⟩

⟦1,3⟧ ∋ 2,5

⟨⋯ 1 ⋯ 4 ⋯⟩

⛔Avoid

⟨⋯ ? ⋯ 5 ⋯ (?+1)⟩ (?≠4)

max {p3, p2, p0} = 5

#125034_v2.11

2026-01-02 Q1(v=0)

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨? 1 ⋯ (?−2) ⋯ 3 ⋯⟩ (?≠3)

⟨? ⋯ 0 (?−1) ⋯ 5 ⋯⟩ (?≠1)

#125034_v2.11

2026-01-02 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

min ⊢3⊣ = 1

⟨⋯ Perm(0,2) ⋯⟩

Jump(3,5) ≤ 2

{p3, p2, p0} = ? + {0,2,3}

⛔Avoid

⟦0,1⟧ ∋ 3,5

max ⊢2⊣ ≤ 3

#125034_v2.11

2026-01-01 Q1(v=1)

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

4th → a, 2nd → b, |a-b|=1

4th → a, 3rd → b, |a-b|=4

2nd → a, 0th → b, |a-b|=1

⛔Avoid

⟨⋯ ᵃb ⋯⟩, |a-b|=3

⟨⋯ ᵃb ⋯⟩, |a-b|=0

#125034_v2.11

2026-01-01 WR

Rearrange the digits in ⟨125034⟩ to meet the rules below.

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

⟨ ²ⁿᵈa ⁰ᵗʰb ⟩, (ab)₁₀ ≥ 43

⟨ ⁵ᵗʰ= ⁴ᵗʰ↑ ³ʳᵈ↓ ²ⁿᵈ↓ ¹ˢᵗ↑ ⁰ᵗʰ= ⟩ after 5−⟨⇌⟩

4th → 1|4|5

5th → a, 2nd → b, ab=0

⛔Avoid

⟨ ³ʳᵈa ⁰ᵗʰb ⟩, (ab)₁₀ ≤ 34

#125034_v2.11

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