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Binairo Full Count: Half and Half

The full count technique says: every line is half one colour and half the other, so once a line has half of one colour, every other square in it is the other. It’s easy to miss, especially late in a puzzle, when lines fill up fast.

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This is the third of the Binairo techniques.

The rule

  1. Count the yellow and the teal in a row or column.
  2. If either colour has reached half the line’s length, fill every empty square with the other colour.
Full count: a row with its three teal A row of six: teal, yellow, teal, empty, empty, teal. That's three teal, half the row, so the two empty squares, 4 and 5, are yellow. 1 2 3 4 5 6 1
Teal in squares 1, 3 and 6 is half the row, so squares 4 and 5 are yellow.

In a real puzzle

On the 10×10 every technique page follows, the first full count comes at step 22. Column 2 has yellow in rows 1, 2, 5, 6 and 9: five, half of its ten squares. Its two empty squares, rows 8 and 10, are teal.

Step 22: full count Hard level 2 at step 22, with column 2 highlighted and the squares this step settles marked. 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10
Step 22: column 2 has its five yellow, so rows 8 and 10 are teal.

How often you’ll need it

Every one of the game’s 150 levels uses it: about 9 times per puzzle on Easy and Medium, and 11 on Hard. On the 10×10 here it’s 12 of the 57 moves. Most come late: across the levels, about three quarters of the full counts in a solve happen in its second half.

Next steps

Questions

How many of each colour does a line need?

Half its length: three of each on a 6×6, four on an 8×8, five on a 10×10.