Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was thinking of.

[This is an exercise for practice from the Hungarian KöMaL magazine, September 2000 issue. You'll find many other challenging problems in English on the KöMaL website.]