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Light Up: A Number That Needs Every Square

A number with just enough room left for the bulbs it still needs has a bulb in every one of those squares. A 4 always does; so does a 3 on an edge or a 2 in a corner.

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This is one of the Light Up techniques. Each page shows its technique on the same 12×12 from the game, Hard level 4.

The rule

  1. Find a number, and count the bulbs it still needs.
  2. Count the white squares touching it that could still take one: not dotted, not lit.
  3. If the two counts match, every one of those squares gets a bulb.

In a real puzzle

On the 12×12, it’s first needed at step 5. The 2 in row 3, column 6 has a black square above it and the 1 to its left, so only two white squares touch it: below it and to its right. Both get bulbs.

Hard level 4, step 5 number-needs-all: bulb row 4, column 6 & row 3, column 7 (from row 3, column 6) 2 1 0 1 2 1 0 1 2 0 1 1 1 1 4 0 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 5: the 2 has only two white squares beside it.

How often you’ll need it

On every one of the game’s 150 levels: 3.5 times per Easy level on average, 6.6 on Medium and 8.2 on Hard. It’s 9 of the 42 steps on the 12×12 here.

Next steps

Questions

Which numbers need every square?

A 4 always does. So does a 3 on an edge, a 2 in a corner, or any number whose other squares are black, off the grid or already ruled out.