Choose a number, do a series of operations on it, everyone gets the same answer?

Question

I remember a class where the teacher told each student to choose a number at random. Then the teacher instructed the students to perform a series of operations on the number (e.g. multiply your number by 14, substract one, etc.) At the end, everyone had the same answer despite starting with different numbers. Who can find some equations like that? (Multiply by zero is cheating.)

Answer 1

This often uses the property that the sum of the digits of n = n (mod 9), for example:

Pick a number (n)
Add 14 (n+14)
Multiply by 9 (9*(n+14))
Subtract 8 (9*(n+14)-8)
Add up all the digits (9*(n+14)-8 mod 9 = 1 mod 9)
Add 5 (6 mod 9)
Add up all the digits again (6)
Subtract 6... You now have the number zero!

Answer 2

Be careful when using Benoit's method that some smart-aѕѕ doesn't choose a number like 2,222,209 or -14.

Another one along similar lines:
Choose a (multiple-digit) number (with all digits not the same).
Jumble up the digits to form a new number.
Subtract the smaller number from the larger.
Multiply by 2.
Add 18.
Add the digits in this new number.
If the result has more than 1 digit add the digits in the result, and keep repeating this until the result has one digit.
(Its this last step that must be included in Benoits algorithm for all positive numbers to work)
The answer is 9.