I’m growing an app that generates puzzle video games day-after-day (https://125034.pages.dev/).
Their fundamental kind could also be considered as Wordle in math, Sudoku in 6 grids, or Einstein’s Riddle in 1 row.

If at the moment was 1713-11-07 and the app model was v1.0.0, it will produce the next puzzle:

WR 1713-11-07

Rearrange the digits in ⟨125034⟩ to fulfill the principles beneath.

⟨fifth 4th third 2nd 1st 0th⟩

✅Match
⟨⋯ 2 ⋯ ? 3 ⋯ (?+5)⟩ (?≠3)

⛔Avoid
1st → a, 0th → b, |a-b|=1
4th → 1|4|5
third → a, 0th → b, a+b=2+5n
⟨⋯ 4 ⋯ 1 ⋯⟩
third → a, 2nd → b, |a-b|=1

#125034 v1.0.0

In different phrases, we’re requested to discover a permutation of ⟨125034⟩ in order that the entire required patterns are matched and the entire forbidden patterns are prevented.

What is the reply and the way do you strategy it?