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?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
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?
Starting with two basic vector steps, which destinations can you reach on a vector walk?