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CS Unplugged activity

Binary Battleship: 16 by 16

About 35 minutesPairPencil

The harder version of Binary Battleship: the same game, but the grid is twice as wide and twice as tall, so every label needs a fourth binary digit. If you haven’t played the 8 by 8 version yet, play that one first: it explains the rules this page assumes you already know.

How to read a 4-bit label

This grid has 16 rows and 16 columns, so each label needs four binary digits instead of three. Now the places are worth 8, 4, 2, and 1:

Place value8421
Digit1010

Add up the place value under every 1 digit: 8 + 0 + 2 + 0 = 10. So the label 1010 means row (or column) 10. Four binary digits, each 0 or 1, give 2 x 2 x 2 x 2 = 16 different labels: exactly enough to number every row and column from 0 to 15.

Each of you already has a fleet drawn on your own “My ships” grid below, so there’s no setup: just start calling shots.

Player A

Keep this page hidden from Player B.

Player B

Keep this page hidden from Player A.

Want a different kind of challenge? Make a fresh set of fleets and pick the hex challenge level: it swaps every binary label for a single hex digit, 0 through F, standing for the same 16 rows and columns.

Check your answers

After the game.

  1. The biggest label is 1111, which is 8 + 4 + 2 + 1 = 15.
  2. Four digits, each 0 or 1, give 2 x 2 x 2 x 2 = 16 different labels, so 16 rows: 0 through 15.
  3. It added 8 rows, going from 8 rows to 16. Each extra bit doubles how many labels are possible, so the 8 by 8 grid’s 8 rows became 16, not 9.

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