As a kid, I liked arithmetic function machines that "magically" force a particular output or allow one to quickly deduce the input from the output. These are usually based on non-obvious (to a kid) identities. I would invent my own and then ask family members to play along. I'm not sure if this sort of puzzle game has a name?

A simple example:

- Multiply your number by 2

- Add 10

- Divide by 2

- Subtract the original number

Sounds like a great game; I have "games" during my 6yo's bathtime. These games have now evolved to multiplying numbers by four (or three, two), subtraction and addition of 2-digit numbers, etc. Also a few word games (Rhymes, etc)

Since it's in the bath, no paper and pencils are used, but it's good fun for him.

Haha I played this game with my daughter the whole time she was growing up. She loved it.

Reverse-engineering is fun.