These problems are very simple and surprisingly fun to work with. Their purpose is to develop "thinking culture" (Arnold says this in the intro). He also writes that "the worst at solving these simple problems are Nobel and Fields prize winners" :) Now, I think that's Russian hyperbole or poetic licence, if you will, but it does illustrate an issue I run into nearly daily teaching maths to 13 - 15 year olds: Some of the kids think in ways I have a hard time understanding and often solve problems in ways which are difficult for me to grok because they are not using mathematical language to explain what they're doing. This happens especially with kids who generally perform poorly in maths. They solve problems similar to these in ways I have a lot of trouble understanding because it's like we are speaking two different languages. These problems are trivially easy if you translate them into simple equations (the ones I've done, anyway). The problem is I don't think that's what Arnold means when he says "Thinking culture", so I suspect I might be cheating ;)

Edit: Nr. 13 is wonderful :)