How does this maths "trick" work?

I've come across a few of these before in the great email-forwarding
madness of the internet, and was wondering how this one
(http://digicc.com/fido/) works:

1. Think of a number three or four digits long (eg. 725)
2. Jumble all the digits to make another number (572)
3. Subtract the smaller from the larger (153)
4. Pick one of the numbers (3), remember it, and remove it (15)
5. Jumble the remaining digits again (51)

The machine spits out "3", the correct answer from step 4

Psychic 7-up at it's finest.

.

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