A cat on the stair
Analysing some possible trajectories for a cat stopped over a sliding stair (think about the particular cases and try them with the applet bellow).
This activity is linked with a Kahoot quizz, that you can get in https://play.kahoot.it/#/k/85da17b4-936b-4a51-bbff-26a5b18fa60f.
You can see a deep approach for this problem in
http://clubes.obmep.org.br/blog/problemao-a-volta-do-gatinho/ (in portuguese).