Rearrange the digits in ⟨125034⟩ to meet the rules below.
⟨ ⁵ᵗʰ▨ ⁴ᵗʰ▨ ³ʳᵈ▨ ²ⁿᵈ▨ ¹ˢᵗ▨ ⁰ᵗʰ▨ ⟩
✅Match
⟨⋯ 5 ⋯ 1 ⋯ 0 ⋯⟩
⟨⋯ 2 ⋯ 4 ⋯ 5 ⋯⟩
⛔Avoid
⟨⋯ 3 ⋯ 4 ⋯⟩
⟨? ⋯ 5 ⋯ (?+1) ⋯⟩ (?≠4)
#125034_v2.14
┌───┬───┬───┬───┬───┬───┐
│5th│4th│3rd│2nd│1st│0th│▒
╞═══╪═══╪═══╪═══╪═══╪═══╡▒
Step 1 │ 2 │ │ │ │ │ │▒
├───┼───┼───┼───┼───┼───┤▒
Step 2 │ 2 │ 4 │ │ │ │ │▒
├───┼───┼───┼───┼───┼───┤▒
Step 3 │ 2 │ 4 │ 3 │ │ │ │▒
├───┼───┼───┼───┼───┼───┤▒
Step 4 │ 2 │ 4 │ 3 │ 5 │ │ │▒
├───┼───┼───┼───┼───┼───┤▒
Step 5 │ 2 │ 4 │ 3 │ 5 │ 1 │ │▒
├───┼───┼───┼───┼───┼───┤▒
Step 6 │ 2 │ 4 │ 3 │ 5 │ 1 │ 0 │▒
└───┴───┴───┴───┴───┴───┘▒
▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
Proof of 2026-09-01 WR
══════════════════════
By ✅「⟨⋯ 5 ⋯ 1 ⋯ 0 ⋯⟩」 and ✅「⟨⋯ 2 ⋯ 4 ⋯ 5 ⋯⟩」, we have
(1) 2 is to the left of 0,1,4,5.
On the other hand, to avoid ⛔「⟨⋯ 3 ⋯ 4 ⋯⟩」, we need to match the following pattern:
(2) ⟨⋯ 4 ⋯ 3 ⋯⟩.
In view of (1) and (2), we see that 2 is to the left of all other digits. Therefore, 2 is at the leftmost corner:
┌───┬───┬───┬───┬───┬───┐
│ 5■│4th│3rd│2nd│1st│0th│▒
╞═══╪═══╪═══╪═══╪═══╪═══╡▒
Step 1 │ 2 │ │ │ │ │ │▒
└───┴───┴───┴───┴───┴───┘▒
▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
--- Idle ---
┌───┬───┬───┬───┬───┬───┐
│ 1 │ │ 5 │ 0 │ 3 │ 4 │
└───┴───┴───┴───┴───┴───┘
Now ⛔「⟨? ⋯ 5 ⋯ (?+1) ⋯⟩ (?≠4)」 implies the following required pattern:
(3) ⟨2 ⋯ 3 ⋯ 5 ⋯⟩.
Combining ✅「⟨⋯ 5 ⋯ 1 ⋯ 0 ⋯⟩」, (2), and (3), we finish by
┌───┬───┬───┬───┬───┬───┐
│5th│ 4■│ 3■│ 2■│ 1■│ 0■│▒
╞═══╪═══╪═══╪═══╪═══╪═══╡▒
│ 2 │ │ │ │ │ │▒
├───┼───┼───┼───┼───┼───┤▒
Step 2 │ 2 │ 4 │ │ │ │ │▒
├───┼───┼───┼───┼───┼───┤▒
Step 3 │ 2 │ 4 │ 3 │ │ │ │▒
├───┼───┼───┼───┼───┼───┤▒
Step 4 │ 2 │ 4 │ 3 │ 5 │ │ │▒
├───┼───┼───┼───┼───┼───┤▒
Step 5 │ 2 │ 4 │ 3 │ 5 │ 1 │ │▒
├───┼───┼───┼───┼───┼───┤▒
Step 6 │ 2 │ 4 │ 3 │ 5 │ 1 │ 0 │▒
└───┴───┴───┴───┴───┴───┘▒
▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒
--- Idle ---
┌───┬───┬───┬───┬───┬───┐
│ │ │ │ │ │ │
└───┴───┴───┴───┴───┴───┘
Q.E.D.
#125034_v2.14