This will become a regular feature. We’ll start with old chestnuts, and once we are finished with them, we’ll get to new chestnuts. Please write in with your solutions! There will be exciting prizes for the best solutions, and they will be published.
Problem 1. Without using a calculator, work out which is larger, or .
Problem 2. How many squares (of any size) are there in an 8 by 8 chessboard? What about an 8000 by 8000 chessboard?