4x4 Tile Mover Sudoku
(Published on 28. July 2021, 18:26 by Sktx)
I am experimenting with this new type of constraint, and because it is a very hard variant to set, I figured I should start with a 4x4. I must thank Trevor Tao and his/her "Order is important" Sudoku variant for the inspiration, proving that time/order of steps can play a role in sudoku variants.
F-puzzles link
CtC app link
Penpa+ link
==== RULES ====
4x4 Sudoku rules apply : fill the grid with digits 1 to 4 appearing each once in every row, column, and 2x2 box.
Tile-Mover rules apply :
- cells with cages are tiles.
- A tile marked with digit n must be moved n orthogonal steps away, through a n-cell path (not including the original cell), and at the end of its move the digit n must appear.
- A tile path doesn't need to be a shortest path to its end, but can not use twice the same cell (no loop or backtrack on the path).
- Each tile must be moved all the way at once, so it needs to have a full free path to its final position.
- Tiles can not go through dark grey cells, nor through other tiles. Thus, before being moved, a tile blocks its cell for the other tiles. Once a tile has been moved, it frees its starting cell, but blocks its end cell for the rest of the solve.
- It is up to the solver to decide in which order the tiles should be moved. The solution code needs for you to keep this order in mind.
Not all possible tiles are given (no negative constraint).
Solution code: Digits from row 4 (left to right), followed by the digits marking the tiles, in the order that the tiles had to be moved (if you moved a tile marked [1], then [3], then [4], etc, put 134etc...). No space. 11 digits total.
Comments
on 2. August 2021, 16:40 by PrimeWeasel
Very cool!
on 29. July 2021, 18:58 by shcuF
Cute little puzzle :)
@shcuF : Thanks a lot ! The 9x9 version just came out :). It is harder but should be approachable if you solved this 4x4 first.
on 29. July 2021, 00:56 by Sktx
as pointed out by @Klomp, I added in the rules a reminder that the order of the tiles should be kept in mind for the solution code
on 29. July 2021, 00:50 by Zombie Hunter
When solving in Penpa I put a corner digit to indicate which digit I moved at which time. Made entering the solution code easy.
on 28. July 2021, 23:15 by Klomp
Did not like having to keep track of the order in which i moved the tiles, prefer a solution code that can be read from the finished puzzle
@Klomp : hi, and thank you for solving my little puzzle. I understand it is bothersome, and I do not intend to use that kind of solution code if I ever make a 9x9 with this ruleset. However, since it is a 4x4, it can be easy to make several guesses and get away with it by trying a little number of codes... Since I have only 7 tiles, I figured I would make the solution code reflect the logic used in the puzzle, somehow... Thanks for that feedback though, I will keep this in mind for my next one.
