Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!