1. Think of a number.
2. Add 17.
3. Double.
4. Subtract 4.
5. Double.
6. Add 20.
7. Divide by 4.
8. Subtract 20.
9. What number do you have? ..
..
..
..
You should have your original number back.
Why does this work?
Let's use algebra to explain it.
| 1. Think of a number. | Let x = the original number. |
| 2. Add 17. | Then we get x + 17 |
| 3. Double. | We have 2 (x + 17) or 2x + 34 |
| 4. Subtract 4. | Now we get 2x + 30 |
| 5. Double. | Now we have 4x + 60 |
| 6. Add 20. | We obtain 4x + 80 |
| 7. Divide by 4. | We get x + 20 |
| 8. Subtract 20. | We get x, the original number |