In the last episode (#20), we saw that just one extra bit, the parity bit, can tell us if an error has occurred in the message we send. Building on this idea, mathematician Richard Hamming asked a natural but brilliant question:

Can we not only detect errors, but also correct them just by adding a few extra parity bits?

Before diving in, make sure you’ve read episode #20—this builds directly on that.

So here’s the challenge!

Let us try to answer this the hard way.