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Shikaku: Only One Fit

A number with only one rectangle left that fits gets that rectangle. It places every rectangle in the end: the other techniques just clear the way for it.

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This is one of the Shikaku techniques. Each page shows its technique on the same 12×12 from the game, Hard level 2.

The rule

  1. Pick a number, and list the rectangles of its area that hold its square.
  2. Cross out any that hold another number, run off the grid, or overlap a rectangle already drawn.
  3. If only one is left, draw it.

In a real puzzle

On the 12×12 every technique page follows, it’s the very first move. The 10 in row 11, column 5 has only one rectangle of ten squares that fits: two rows by five columns, in the bottom-left corner.

Hard level 2, step 1 only-fit: the 10 in row 11, column 5 is 2x5 from row 11, column 1 10 7 12 7 8 9 12 2 2 12 3 8 4 12 10 2 12 8 2 2 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12
Step 1: the 10 has only one rectangle that fits (dashed).

How often you’ll need it

On every one of the game’s 150 levels, and more than any other technique: 12.3 times per Easy level on average, 19.9 on Medium and 26.8 on Hard. It’s 20 of the 28 steps on the 12×12 here.

Next steps

Questions

How do I list a number's rectangles?

Run through the ways its area divides (a 6 is 1×6, 2×3 and the same turned round), and for each, every position that holds the number’s square. Keep the ones that hold no other number and overlap nothing already drawn.