Challenge Level

To make a Magic W you have to put the numbers 1, 2, ...,9, one in each circle, so that each row of three numbers has the same total. Experiment to find as many different magic totals as you can using the interactivity from the Magic W problem.

Prove that if you have a Magic W and you replace each of the numbers by 10 minus that number then the new W is also magic. What will its magic total be?

Prove that you cannot form a Magic W with a total of 12 or less. Also prove that you cannot form a Magic W with a total of 18 or more.