Today, we’re down with the digits. Here are three elegant number puzzles, each nudging your brain to think creatively in different ways. 1. Well balanced What number equals the average of its digits? 2. The painted cube A large wooden cube is painted on all of its faces. I divide the cube into a thousand mini cubes by slicing it nine times in each dimension. How many cubes have no paint on them? The bad way to calculate the answer is to start with 1000 cubes and subtract the ones with paint: 100 x 2 from the first set of opposing faces, 80 x 2 from what’s left of the next two opposing faces and 64 x 2 from what’s left of the remaining two faces. The puzzle is to find a much faster way to get a solution. It involves a simpler calculation that you are more likely to be able to do in your head. 3. Clever countdown You are playing a game with a friend, in which you start at the number 100 and take turns to deduct a number between 1 and 7. The winner is the person that lands on zero. Which number do you choose first to be assured of winning? I’ll be back at 5pm UK with the solutions. PLEASE NO SPOILERS. Share your favourite numbers. UPDATE: Read the solutions here. Thanks to these readers for suggesting today’s questions: 1. David Grossman 2. Richard Connor, professor of computer science at the University of St Andrews (who said it is his favourite puzzle). 3. Chris Eddlestone (who remembers it from his Oxbridge interview.) I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
Author: Alex Bellos