Imagine you have a large supply of 3kg and 8kg weights. How many of
each weight would you need for the average (mean) of the weights to
be 6kg? What other averages could you have?
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
Charlie likes to go for walks around a square park, while Alison
likes to cut across diagonally. Can you find relationships between
the vectors they walk along?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?