Hamming Cards

Choose a number. Use cards A – D without lying. How many numbers are covered after each step?

Choose a number. Use cards A – G. You can lie once. The cards should reveal your number.

Does this always work? Try lying twice. Try not lying. What happens?

First, try the Hamming Card trick without lying. The cards are designed so that wrong answers are always covered 3 or more times. This means that, when you lie once, one of the cards get flipped. So now all the wrong answers are covered at least twice. But the correct answer is only covered once, allowing the correct answer to show through the window. We can use this idea to fix mistakes when sending messages on the internet. All messages on the internet are turned in sequences of 1s and 0s. But your computer will add a few extra 1s and 0s so that every message contains at least 3 differences. Now, if one digit goes wrong, the correct message will only be 1 digit away. All other messages will be 2 or more digits away. This allows your computer to fix the message by choosing the closest correct answer. This is not a secret code, but it is a code that allows us to transmit messages safely and reliably.