Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
⟨ ¹ˢᵗa ⁰ᵗʰb ⟩, (ab)₁₀ ≥ 30
⟨⋯ ᵃb ⋯⟩, |a-b|=2
4th|3rd|1st|0th → 2
⛔Avoid
1 ∾ 5
⟨⋯ Perm(0,2) ⋯⟩
5th|3rd|2nd|1st → 3
Jump(1,2) ≥ 1
#125034_v2.12
Blog of 125034
Originating from a math proof, 125034 is a game driven by combinatorics, logic, and probability.
2026-02-03 Q1(v=1)
Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
⟨ ⁵ᵗʰa ²ⁿᵈb ⟩, max⟦a,b⟧ = 5
⟨ ⁴ᵗʰ↓ ³ʳᵈ↑ ⟩ after 3×⟨→⟩
⟨ ¹ˢᵗ↑ ⟩ after ⟨←⟩
⛔Avoid
⟨ ²ⁿᵈ↓ ⁰ᵗʰ↓ ⟩ after ⟨←⟩
⟨ ⁴ᵗʰ↓ ²ⁿᵈ↑ ⟩ after 2×⟨→⟩
⟨ ⁵ᵗʰ↓ ⟩ after ⟨←⟩
min {p3, p2} = 1
#125034_v2.12
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
2025-12-01 Ex2
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.
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