Mr. Leon Cranfield taught students at Ned Doman High School in Cape Town South Africa. One day he finished teaching his lesson with a few minutes to spare, so he gave them this puzzle: "Think of any number and write it down, multiply it by 3, then add 6, multiply by 2, divide by 6, subtract the number you thought of, and write down the number you get." When the students were finished he went around the room and asked each student what number they got. Surprise! They all got the same number. What was the number? What's going on here?
Solution
If you build a formula in algebra-speak, you start with , then you get , then , then or , then = then . Subtract your and you have , every time.
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.