# Three for the price of one

While browsing through your local puzzle store, you see something you can't resist: a box which promises two grid deduction puzzles for the price of one!

The vendor explains that the box contains a single numbered grid depicting two uniquely solvable puzzles of different types. The types of puzzles vary from box to box but are specified in each box's instructions.

You fork over the meager sum of one upvote and rush home, giddy with excitement.

Unfortunately, when you arrive home and unbox the grid, you discover that not only does it require assembly, but also that the instructions are missing. All you find are four 2x2 squares which can be connected along their edges.

You feel certain that there is a unique way to combine them into a single grid on which can be played two puzzles of the intended types.

It dawns on you that assembling the grid is itself a puzzle. But that's fine with you—it means you actually got three puzzles for the price of one!

• Are rotations allowed? Commented Mar 9, 2017 at 16:12
• The 2x2 squares are physical parts of a grid that must be assembled. Rotating some of them could make funky the orientations of the numbers in the final grid. If you must rotate, do so by a multiple of 360 degrees. Commented Mar 9, 2017 at 16:16
• Thanks, rotating by a multiple of $360^{\circ}$ is indeed a brilliant idea. :P Commented Mar 9, 2017 at 16:17
• I get the best results when rotating the 3rd square by 720° and the 1st square by NEGATIVE 360°. Your mileage may vary.
– Rubio
Commented Mar 9, 2017 at 17:57

If we assume that one of the puzzles is a sudoku, we are left with only four possible grid constructions because the last two pieces can not be next to each other and have to form the diagonal. I tried slitherlink as the second puzzle which gave a unique solution for only one of those grids. In that grid the three corners with numbers can be solved immediately which quickly leads to the solution.

The solved sudoku then looks like this

There are probably other possible solutions depending on the chosen puzzles.

After trying lots of different puzzles, I might have to take that back. The only one that came close was a fillomino which had one grid with a unique solution if we forbid 4s.

• These are indeed the intended puzzles. But it's actually possible to construct 4 sudokus with the sub grids. Also, it would be nice if you could show a step-by-step solution of the slitherlink. (No need to prove uniqueness or that the other possible sudokus yield non-unique slitherlink solutions.) Commented Mar 9, 2017 at 18:56
• @Silenus Changed the mistake. Do you really think the slitherlink needs a step-by-step solution? I did not add one because I thought it was trivial. I will add it if you feel it needs one.
– w l
Commented Mar 10, 2017 at 7:38
• The answer is good now, no need for the step-by-step. I'm glad you played around trying to find other possible puzzle interpretations. When designing the puzzle, I tried to check against those possibilities. Commented Mar 10, 2017 at 12:16

I think it's the below.

Kind of a rip-off though - it is technically solvable as either a pseudo-sudoku or as a magic number square, with each row and column having the same sum, but both will give you the same results

= = = = = = =
= 2 3 | . . =
= . 1 | 3 . =
= = = | = = =
= . . | 2 . =
= 1 . | . 3 =
= = = | = = =