You initially think of a four digit number.
You choose .
You then 'jumble' up to get for example
Set , therefore .
Let's now look at modulo :
Now here's the trick: You take away one of the digits of and you friend guesses it! How you ask? Well it has to do with being divisible by . A divisibility test for says a number is divisible by if and only if the sum of the digits is divisible by .
So if and you remove for instance your friend will in a sense solve for . He solves . Thus he sees .
There is a bit of a flaw in this trick though: if the number you circled was either or , he has a chance of guessing it right, otherwise he'll get it right every time!