TITLE: Mathematical games interesting to both you and a 5+-year-old child
QUESTION [251 upvotes]: Background: My daughter is 6 years old now, once I wanted to  think on some math (about some Young diagrams), but she wanted to play with me... 
How to make both of us to do what they want ?   I guess for everybody who has children, that question comes up. 
Okay, I said to her: let's play a game which I called "Young diagram" for her: 
we took a sheet of paper and I tried to explain to her what a Young diagram is, she was asked to draw all the diagrams of some size n=1,2,3,4,5...
Question: Do you have some experience/proposals of  "games" which you can play with your children,
which would be on the one hand would make some fun for them, on the other would
somehow develop their logical/thinking/mathematical skills,
and on the other hand would be of at least some interest for adult mathematicians ?
Related MO questions:
“Mathematics talk” for five year olds
it is quite related to the present question, but slightly different -
it is about a single presentation to children, while the present question
is about your own children with whom you play everyday, you can slightly "push",
and so on...
How do you approach your child's math education?
it is also related, but the present questions has a slightly different focus:
games interesting for children and adults. The book  by Alexandre Zvonkine, "Math for little ones" (in Russian here), recommended in  answer there - is really
something related to the present question.
Which popular games are the most mathematical? is NOT directly related,
but may serve as kind of inspiration for answers...

I think Allen Knutson's answer on  “Mathematics talk” for five year olds:

I've spoken (to 5+ years old) about the "puzzles" that Terry Tao and I
  developed for Schubert calculus, like the left two here:

can be a nice example of an answer to the present question as well:
on the one hand there is something to explain to the child and some colorful pictures,
and on the other hand that is about research level math ...

REPLY [2 votes]: You can play Tic-Tac-Toe on the affine plane of order 5. 
Check up PentacTow. 

I have a few further ideas for applications gaming finite geometries
and I take this opportunity to invite whoever codes and have interest in such a project to contact me (the TicatacToe was programmed by my brother, Gal Bader, but he is too busy now).