This very puzzle (an many varients thereof) was the subject of a book called Anno's Hat Tricks, by Mr. Mitsumasa Anno. Somewhere I think I have my old copy.

Mitsumasa Anno also wrote a number of simply wonderful books that I grew up with. Especially Anno's Journey. There are no words in this book, but that makes it all better. If you have kids, get these books for them; if you don't, get them for yourself.