I should have started with my favorite problem. I gave it to different audiences, ages 10 to whatever. Usual results are always the same: two or three people do it correct. The problem is many times older than I am. Here it is (more modern variation).
The distance between A and B is 100 km. Two bicyclists start moving simultaneously towards each other from A and B respectively with speeds 10 km/h and 15 km/h. A dog starts running from A at the same moment as bicyclists do with the speed 20 km/h. When it reaches the second bicyclist, it turns back, runs until meeting the first one, turns again etc. The dog runs back and forth until bicyclists meet. What distance does it run?
As I mentioned above, the number of fifth graders who solved this problem is approximately the same as the number of high school seniors. BTW the results were the same in USA, Russia, and Ukraine :-)
I remember you giving us problems like this one all the time when we were little. Every time we were on the go (which we often seemed to be), Yulia and I used to ask you to give us more problems. I really hope that you can remember (and post here) most of the good ones so that we can give them to our kids!
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