# 13-by-13 SIKAKU puzzle

A SIKAKU puzzle consists of a square or rectangular grid in which some of the cells contain a one or two digit number. To complete the puzzle, a Solver must divide the puzzle into a number of rectangles so that each rectangle contains exactly one of the numbers, and that number must be equal to the area of the rectangle which contains it. Each puzzle has a unique solution which does no require any guesswork to achieve.

Example :

Solve This

• It seems like an easier version of nurikabe – justhalf Oct 16 '17 at 11:40
• @justhalf It's quite different. The regions have to be rectangular, and the divisions are made with edges, instead of blocks. – Matthew Jensen May 4 at 4:37
• Yep, the extra restriction is what made me say it is an easier version of nurikabe. – justhalf May 4 at 5:28
• Why nurikabe? Shikaku has been an existing genre for a long time, plus, nurikabe requires shading cells – Anonymus 25 May 4 at 8:48

It was really fun!!

The solution to puzzle is:

Step 1:

Some trivial deductions based on numbers which must be part of 1×N rectangles, and the fact that each rectangle can only have one number.

Step 2:

The 25 must be 5×5, and there's only one way to let it be. This forces the 5 above it to stretch to the corner as no other number can reach. It also squeezes the 7, 4, and 10 below it and lets them be resolved.

Step 3:

The 16 must be 4×4; 2×8 is impossible. This ends up forcing a nearby 12 and 10.

Step 4:

Various reachability deductions in the bottom-left corner. Only the 8 can get to the corner, so it must stretch all the way there. Then only the 4 can get to the square above the 8, so we can resolve it. Finally only the 12 can stretch to R11C1, so it does so.

Step 5:

More reachability, along the top this time: the 8 to R1C1, and the 12 to both R1C5 and R1C8.

Step 6:

The 9 now needs to be 3×3. This lets us resolve the 3 and 8 near it.

Step 7/solution:

The rest is trivial packing logic.