2026-08-04 WR

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

⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩

✅Match

Jump(1,3) = 3

⟦2,3⟧ ∋ 0,4

⟦1,3⟧ ∋ 0,5

⛔Avoid

⟨     ³ʳᵈ↓       ⟩ after ⟨→⟩

5th → 0|3|4

⟦0,5⟧ ∋ 4

#125034_v2.14

       ┌───┬───┬───┬───┬───┬───┐
       │5th│4th│3rd│2nd│1st│0th│▒
       ╞═══╪═══╪═══╪═══╪═══╪═══╡▒
Step 1 │ 2 │   │   │   │   │   │▒
       ├───┼───┼───┼───┼───┼───┤▒
Step 2 │ 2 │ 1 │   │   │   │   │▒
       ├───┼───┼───┼───┼───┼───┤▒
Step 3 │ 2 │ 1 │   │   │   │ 3 │▒
       ├───┼───┼───┼───┼───┼───┤▒
Step 4 │ 2 │ 1 │ 0 │   │   │ 3 │▒
       ├───┼───┼───┼───┼───┼───┤▒
Step 5 │ 2 │ 1 │ 0 │   │ 4 │ 3 │▒
       ├───┼───┼───┼───┼───┼───┤▒
Step 6 │ 2 │ 1 │ 0 │ 5 │ 4 │ 3 │▒
       └───┴───┴───┴───┴───┴───┘▒
        ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒

Proof of 2026-08-04 WR
══════════════════════

There are two ways to match ✅「Jump(1,3) = 3」:

    ┌───┬───┬───┬───┬───┬───┐
    │5th│4th│3rd│2nd│1st│0th│
    ╞═══╪═══╪═══╪═══╪═══╪═══╡
(1) │1 3│   │   │   │1 3│   │
    ├───┼───┼───┼───┼───┼───┤
(2) │   │1 3│   │   │   │1 3│
    └───┴───┴───┴───┴───┴───┘

--- Idle ---
┌───┬───┬───┬───┬───┬───┐
│   │ 2 │ 5 │ 0 │   │ 4 │
└───┴───┴───┴───┴───┴───┘

As ✅「⟦2,3⟧ ∋ 0,4」 and ✅「⟦1,3⟧ ∋ 0,5」 imply that 0,4,5 are not in corners, we have

    ┌───┬───┬───┬───┬───┬───┐
    │5th│4th│3rd│2nd│1st│0th│
    ╞═══╪═══╪═══╪═══╪═══╪═══╡
(3) │1 3│   │   │   │1 3│ 2 │
    ├───┼───┼───┼───┼───┼───┤
(4) │ 2 │1 3│   │   │   │1 3│
    └───┴───┴───┴───┴───┴───┘

--- Idle ---
┌───┬───┬───┬───┬───┬───┐
│   │   │ 5 │ 0 │   │ 4 │
└───┴───┴───┴───┴───┴───┘

By ✅「⟦2,3⟧ ∋ 0,4」, there are at least two digits between 2 and 3. It follows that

    ┌───┬───┬───┬───┬───┬───┐
    │5th│4th│3rd│2nd│1st│0th│
    ╞═══╪═══╪═══╪═══╪═══╪═══╡
(5) │ 3 │   │   │   │ 1 │ 2 │
    ├───┼───┼───┼───┼───┼───┤
(6) │ 2 │ 1 │   │   │   │ 3 │
    └───┴───┴───┴───┴───┴───┘

In view of ⛔「5th → 0|3|4」, case (6) holds actually. Therefore, we get

       ┌───┬───┬───┬───┬───┬───┐
       │ 5■│ 4■│3rd│2nd│1st│ 0■│▒
       ╞═══╪═══╪═══╪═══╪═══╪═══╡▒
Step 1 │ 2 │   │   │   │   │   │▒
       ├───┼───┼───┼───┼───┼───┤▒
Step 2 │ 2 │ 1 │   │   │   │   │▒
       ├───┼───┼───┼───┼───┼───┤▒
Step 3 │ 2 │ 1 │   │   │   │ 3 │▒
       └───┴───┴───┴───┴───┴───┘▒
        ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒

--- Idle ---
┌───┬───┬───┬───┬───┬───┐
│   │   │ 5 │ 0 │   │ 4 │
└───┴───┴───┴───┴───┴───┘

Then, there is only one way to avoid ⛔「⟨     ³ʳᵈ↓       ⟩ after ⟨→⟩」:

       ┌───┬───┬───┬───┬───┬───┐
       │5th│4th│ 3■│2nd│1st│0th│▒
       ╞═══╪═══╪═══╪═══╪═══╪═══╡▒
       │ 2 │ 1 │   │   │   │ 3 │▒
       ├───┼───┼───┼───┼───┼───┤▒
Step 4 │ 2 │ 1 │ 0 │   │   │ 3 │▒
       └───┴───┴───┴───┴───┴───┘▒
        ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒

--- Idle ---
┌───┬───┬───┬───┬───┬───┐
│   │   │ 5 │   │   │ 4 │
└───┴───┴───┴───┴───┴───┘

Finally, to avoid ⛔「⟦0,5⟧ ∋ 4」, we finish by

       ┌───┬───┬───┬───┬───┬───┐
       │5th│4th│3rd│ 2■│ 1■│0th│▒
       ╞═══╪═══╪═══╪═══╪═══╪═══╡▒
       │ 2 │ 1 │ 0 │   │   │ 3 │▒
       ├───┼───┼───┼───┼───┼───┤▒
Step 5 │ 2 │ 1 │ 0 │   │ 4 │ 3 │▒
       ├───┼───┼───┼───┼───┼───┤▒
Step 6 │ 2 │ 1 │ 0 │ 5 │ 4 │ 3 │▒
       └───┴───┴───┴───┴───┴───┘▒
        ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒

--- Idle ---
┌───┬───┬───┬───┬───┬───┐
│   │   │   │   │   │   │
└───┴───┴───┴───┴───┴───┘

Q.E.D.

#125034_v2.14