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!
Answer
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.
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