A child aims a phone at a cardboard package whose teal square code has one scratched tile.

How can a damaged message heal itself?

One tiny scratch. Can the message be trusted?

The receiver never saw the original. How could it know what changed?

A sender can tuck a few helper tiles beside the message. They travel together to the receiver.

Teal message tiles and smaller gold helper tiles travel together between two indigo devices.

One helper can remember a row’s promise: does it contain an odd or even number of lit squares?

Four lit squares: the helper promises EVEN.

Put one helper beside every row and below every column. Now each square has two checker directions.

Tap to place the helpers around the grid.

Try one flipped square. Its bad row and bad column cross in exactly one place.

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New test: two marked squares will flip together. They sit in different rows and different columns.

Everything else stays the same. What will the checker geometry reveal?

Two flips. Two row helpers. Two column helpers.

When both marked squares flip, what can this simple row-and-column checker grid do?