Problems for Children from 5 to 15

V. I. Arnold:

I put these problems onto paper in Paris in spring 2004 when Russian Parisians asked me to help their young children gain the thinking culture tra- ditional for Russia.
I am deeply convinced that this culture is most of all cultivated by early independent reflection on simple, but not easy questions similar to those below (problems 1, 3, 13 are the most recommended).

My long experience has shown that, very frequently, dimwits falling at school behind solve them better than A-grade pupils, since – for their survival at the back of the classroom – they must permanently think more than required “for governing the whole Seville and Granada”, as Figaro used to say about himself, while A-graders cannot catch “what should be multiplied by what” in these problems. I have also noticed that five year old kids solve similar problems better than pupils spoiled by coaching, which in their turn cope with the questions better than university students used to swotting who anyway beat their professors (the worst in solving these simple problems are Nobel and Fields prize winners).