Parity row repair: rules and printable materials

Recover one missing binary digit by checking even row and column totals. Detect mistakes without pretending every error can be repaired.

Players

1–6 cooperative

Plan for

10–15 minutes

Bring

Printed binary grid and pencil

Read the message and checks

The data area has three rows: 1,0,1; 0,1,1; 1,1,0. The host key retains the full message. Each row has a check digit written at the right so that the number of ones in that row, including its check, is even. Each column has its check beneath the data so that its total ones is also even. Do not treat a check digit as an extra data cell.

Recover one known erasure

For the player starter the middle data cell, row two column two, is replaced by a question mark. All three row checks and all three column checks are zero. Row two currently has one visible one; the missing bit must therefore be one to make the row even. Column two independently confirms that choice. Write the recovered bit and both counts before looking at the host key.

Check every line

After filling the erased cell, count all three data rows with their row checks and all three data columns with their column checks. Every count should be even. Two inconsistent clues mean the stated one-erasure assumption is not met or a check was copied incorrectly. Do not change several visible data cells until the board merely looks balanced; retain the original message for comparison.

Distinguish a missing bit from an error

A question mark tells you the location of an erasure. A silently flipped bit is a different problem: a single flipped data bit makes one row and one column odd, identifying their intersection only under a promise that exactly one data bit changed. Multiple errors may fool these checks, and an incorrect check bit changes the diagnosis. This activity is a teaching model, not secure encryption.

Share and create

One participant reads cells, another counts ones, and another records the explanation. Use large digits or verbal coordinates instead of requiring color recognition. For a new one-erasure round choose any three-by-three binary data, compute correct even checks, then replace exactly one data cell with a question mark. Keep the key separate. Never erase a check and a data bit while calling it the same starter.

Printable materials

Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.