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Secret Transmissions

Age 14 to 16
Challenge Level

This Venn diagram shows the relationship between the check bits and the message bits. We can use this to work out which digit has been altered. Suppose we find that yacd and zbcd contain an odd number of 1s, and xabd contains an even number of 1s. We look at the intersection of y, z and not-x (any region that x isn't in), which is c. This therefore tells us that c has been altered in transmission.