# An Incomplete Puzzle

I'm sorry to offload some of my work as the puzzle creator on to you solvers. (No, I'm not.) At least there's only one clue missing, right? EDIT: When the puzzle is ready to be solved, there will be six regions with clues instead of five, and any number of unclued regions. Apologies to Eric Tressler.

Complete the puzzle, and then complete the puzzle.

Check mark goes to one who completes the puzzle correctly with a full explanation.

To begin with,

Each pair is either {2,6} or {3,5}. The partitions of 8 into five parts, no four equal: 11123, 11222. The upper zigzag cannot be 11222, because then a 3 has to go in the upper cell of the lower zigzag and it can't be completed.

Continuing,

This lets us complete the lower zigzag, the upper zigzag, and then the pair on the left. The 3-part piece has no 1s, and at most one 2. {2,3,3} is the only solution. This means the upper pair cannot be {3,5}, but is instead {2,6}, and a 2 is already blocking the right cell. We can place the final 1 uniquely in the lower right, as the other five have been placed.

This gets us here:

The new region

has to be a pair touching one the upper right cells with "3" as an option, because an 8+ made out of the remaining numbers must be a {3,5}. We can rule out any regions strictly contained in the upper-right 2 by 2 block, because

these are both valid:

Since

the cells below that 2 by 2 block only have {4,6} as options and not {3,5}, we can rule those out also.

We have ruled out these regions:

If we try the lower of the remaining regions, we get:

stuck.

So we are left with the upper one, for:

The new region

is an 8+, and it is easy to complete the puzzle with this region.

• Mea culpa on the question being unclear; I've updated it now. My intention was that the missing piece is one final clued region to go with the current five (leaving any number of regions unclued, like the single-cell area) Commented May 19, 2018 at 15:13
• I've edited out the old (incorrect) answer, as the semi-detailed correct answer is long enough on its own. Commented May 19, 2018 at 17:35