The walkthrough
Every step below was produced by our solver using only human techniques, and every explanation describes the exact reason the move is certain.
Cells claimed by reachOverlap / new rectangleRemaining options
- Step 1Only optionThe 9 at row 1, column 2 has only one possible rectangle from the start — every other shape would cross the edge of the grid or swallow another number. Draw the 3×3 rectangle.
- Step 2Only optionThe 4 at row 1, column 6 started with 2 possible rectangles, but the rectangles and claimed cells around it now rule out all but one. It must be 4×1.
- Step 3Only optionThe 6 at row 2, column 4 started with 6 possible rectangles, but the rectangles and claimed cells around it now rule out all but one. It must be 2×3.
- Step 4Only optionThe 2 at row 2, column 6 started with 2 possible rectangles, but the rectangles and claimed cells around it now rule out all but one. It must be 2×1.
- Step 5Only optionThe 10 at row 3, column 6 has only one possible rectangle from the start — every other shape would cross the edge of the grid or swallow another number. Draw the 2×5 rectangle.
- Step 6Only optionThe 3 at row 4, column 3 started with 4 possible rectangles, but the rectangles and claimed cells around it now rule out all but one. It must be 3×1.
- Step 7Unreachable cellsThe highlighted cell can only be reached by the 4 at row 5, column 3 — no other number has a rectangle that covers it. So it belongs to the 4, and any option of the 4 that misses it is ruled out.
- Step 8Unreachable cellsThe highlighted cell can only be reached by the 2 at row 6, column 4 — no other number has a rectangle that covers it. So it belongs to the 2, and any option of the 2 that misses it is ruled out.
- Step 9Unreachable cellsThe highlighted cell can only be reached by the 3 at row 7, column 5 — no other number has a rectangle that covers it. So it belongs to the 3, and any option of the 3 that misses it is ruled out.
- Step 10Unreachable cellsThe 3 highlighted cells can only be reached by the 6 at row 6, column 1 — no other number has a rectangle that covers them. So they belong to the 6, and any option of the 6 that misses them is ruled out.
- Step 11OverlapThe 4 at row 5, column 3 still has 3 possible rectangles (dashed), but all of them cover the highlighted cell. Whichever option is right, that cell is part of the 4.
- Step 12Only optionThe 6 at row 6, column 1 started with 5 possible rectangles, but the rectangles and claimed cells around it now rule out all but one. It must be 3×2.
- Step 13Only optionThe 3 at row 7, column 5 started with 4 possible rectangles, but the rectangles and claimed cells around it now rule out all but one. It must be 1×3.
- Step 14Only optionThe 4 at row 5, column 3 started with 4 possible rectangles, but the rectangles and claimed cells around it now rule out all but one. It must be 4×1.
- Step 15Only optionThe 2 at row 6, column 4 started with 4 possible rectangles, but the rectangles and claimed cells around it now rule out all but one. It must be 1×2.
What we used
Notice the rhythm: a few forced rectangles open the grid, reachability and overlap break the deadlock in the middle, and a cascade of forced rectangles finishes it. Most medium Shikaku puzzles follow this shape.
Try it yourself
Solve puzzle #1082
Same grid, interactive board — can you beat the walkthrough?