Think of any number, multiply it by 2, then add 4, multiply by 3, divide by 6, subtract the number you thought of, and the result will be 2. Explain with algebra why this works.
Solution
If you build a formula in algebra-speak, you start with x and you get x+2, then 2x+4, then (2x+4)3 or 3(2x+4), then 3(2x+4)/6, then 3(2x+4)/6 - x. Simplify the expression by good old Please Excuse My Dear Aunt Sally and you'll see that it all boils down to x itself.
It's pretty easy to make up problems like this. Students might like to have a go at it. Another version is to pick a number, do some things, and wind up with your original number.