We play another hypothesis testing game in our family where one player invents a secret rule and gives a single example of a thing that's acceptable. Then the others have to guess other things that might also be acceptable, and the inventor answers yes no. So the inventor starts off with for example

    - Roquefort.

and then the q&a follows

    - Gouda? 
    - no
    - Milk? 
    - no
    - a Nac Mac Feegle? 
    - yes!
    - oh maybe it's everything blue, my backpack! 
    - no
    - the whole universe
    - since that includes gouda, no
    - a cat
    - which cat?
    - greebo
    - then yes
    - it must be something smelly!
    - Yes, that was quick!

It's a bit like Zendo[0], but with .. anything. Could be "words rhyming with -ing" or "flat stuff" etc. etc. Rules have to be fairly simple to be guessable since it's so open, but I did once manage to guess my kid's rule of "things that don't fit into any of the categories made in any of today's rounds of this game".

Some rules can lead to interesting (heated) arguments, which is always entertaining. One thing that could be better is we don't really have a good system for when you can guess a rule vs just giving exemplars, it can get a bit boring if people just guess rules, but OTOH you don't get too far that way since you can't get a "yes" from any other rule than the right one.

[0] https://en.wikipedia.org/wiki/Zendo_(game)

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.