Charlie chose five numbers: $2$, $3$, $4$, $7$, $10$.
He added together pairs of numbers from his set, and got the following totals: $5$, $7$, $9$, $10$, $11$, $12$.
Can you find the totals that Charlie has missed?
Choose your own set of five numbers, and work out all the possible sums of pairs.
How do you know you've found them all?
How many pair sums would there be if you started with six numbers? Or seven numbers? Or ...?
Can you find a set of five different numbers, where the sums of some pairs give the same total?
Can you find a link between the total of any set of five numbers, and the total of their pair sums?
What if you started with a set of six numbers? Or seven? Or ...?
What happens when you choose to add sets of three numbers instead of pairs?...