# 10x10 Choco Banana

Normal Chocolate Banana rules apply.

Rules

1. Paint some of the cells black.

2. Black cells linked orthogonally must always form a rectangle (or a square).

3. Non-blacked cells linked orthogonally must not form a rectangle (or a square).

4. A number indicates the area (the number of cells) of the orthogonally region containing this cell.

Click on the image to use the online solver and view the rules.

• They were right, I just didn't quite like the way it was written
– Sny
Commented Apr 22 at 23:53

The 51 seems pretty unusual:

It has to be unshaded, since a shaded rectangle of size 51 would have a side of length at least 17, which can't fit in this grid. Now since this is unshaded, and its area must contain either R1C9 or R2C10 (or probably both), the 1 in R2C9 must be shaded. This means that the cells orthogonally adjacent to R2C9 must be unshaded, which forces R3C8 to be shaded. Thus its orthogonal neighbors must be unshaded as well.

Looking in the upper left corner:

The 1 in R2C2 must be shaded. If it were not, then R1C2 and R2C1 would have to be shaded, which would force either a non-rectangular shaded region if R1C1 were shaded, or a rectangular unshaded region if not. This now forces R2C2s orthogonal neighbors to be unshaded, and specifically forces R2C3 and R3C2 to be shaded. Now by counting, R3C3 must be shaded as well. This shading must extend either left or down, which forces R4C4 to be unshaded. The grid thus far:

Let's do a little thinking about the clues on the diagonal:

If a clue on the diagonal is shaded, then it cannot be contained in a 1-wide rectangle with any cell north or west of the clue. If clue X were contained in such a shaded rectangle, then it would have X unshaded squares on its north or west side, which would contain an X-1 clue. In particular, this forces the 7 clue to be unshaded. Were it shaded, since 7 is prime it would have to be in a 1x7 rectangle, which by its placement in the grid must contain either the cell north or west of it.

Another look at the 51 clue:

There are only 45 cells strictly above the diagonal, so the 51 must reach around through either R1C1 or R10C10, possibly both. If R10C10 is in this region, then the 8 clue must be shaded, and by the above must be in a 2x4 rectangle, which would force R10C9 to be shaded. Thus the 51 clue cannot get all of its extra cells going around the bottom right corner, so it must go around the top left. This shows R1C1, R1C3 and R3C1 are all unshaded.

Let's look at the 6 clue: