I like combinations of puzzles, so I decided to combine a Sudoku and a Slitherlink.

Below is a 6 by 6 grid. This is filled in with numbers based on the usual rules of sudoku. All of the numbers from 1 to 6 must appear in every row, column, and block. (Blocks are 3 wide and 2 tall.)

The shaded squares are also used as Slitherlink clues. A closed loop must be drawn using the edges of the grid. If the number is 1, 2, or 3, then the loop must pass through exactly that many edges adjacent to the number. However if the number is 4, 5, or 6, that number is treated as if it was 0 and the loop does not pass next to it.

Below is a Slitherlink grid for convenience.

• Truly excellent puzzle, and welcome to the site! Glad to have you. Feel free to browse through our questions about grid-deduction puzzle creation, or hop into chat for more informal discussion. Apr 6, 2021 at 0:16

Step 1:

Place all the 5s. The key one is the hidden single in R6C5. Then a few more hidden singles.

Step 2:

Step 3:

R3C2 can't be a 0 clue in the Slitherlink since it must have an edge in the loop. That force it to be a 1. Several more hidden singles follow.

Step 4:

A 0 Slitherlink clue can't border a 3 in a corner, therefore 6 can't go in R5C6. Now C6 can be filled in with hidden singles.

Step 5:

Step 6:

Either way the 3 in a corner goes, the border between R5C5 and C5C6 must be used. Therefore R5C5 can't be a 0 clue, forcing it to be a 2. I also added in some connectivity Xs.

Step 7:

If R1C2 was either a 3 or a 0 clue, then the border between R1C2 and R1C3 couldn't be used. So it isn't. Then the border between R2C2 and R2C3 must be used, or bad things happen quickly - namely, R1C4 is forced to be a 2, which... doesn't work.

Step 8:

The number of ends entering any one area must be even so that they can match up for the loop. Therefore the 2 in R3C4 must use parallel borders, to avoid creating three hanging ends for the top area. Either way the borders between R2C3-4-5 must all be used.

Step 9:

If the border between R1C3 and R2C3 is used then the 2 in R1C3 can't be satisfied as a Slitherlink clue. Adding an X there allows the top part of the loop to be resolved.

Step 10:

The loop segments at the top give some Sudoku numbers, and with them and some hidden singles the Sudoku grid is resolved.

Step 11: