Please see my comments to the question. This is just one reason why your request might be not very efficient.
One other reason is this: let's assume for a minute that your question will create an enthusiastic competition of ideas among members (I doubt it can happen, but let's assume it). How do you think much time it will take to get good results? I'll predict it as "a lot". A puzzle is really, really hard to invent.
So, you might be much better of doing this:
http://bit.ly/1evBK3g[
^].
[EDIT]
This works out even better:
http://bit.ly/1evE4Y1[
^] ("puzzles", not "games").
And I just recalled one specific puzzle from my childhood:
http://en.wikipedia.org/wiki/Baguenaudier[
^].
I used the form shown on the bottom picture. But you would need to formalize it, which can be hard to do without having the toy in your hands. Actually, the whole process have little except pure recursion.
[END EDIT]
Good luck,
—SA