A proof need not be "formal" to be a perfectly good, elegant, insightful proof. For example, one could observe that an even number of quarters can be formed in

A proof need not be "formal" to be a perfectly good, elegant, insightful proof. For example, one could observe that an even number of quarters can be formed into two rows of the same size, and if you do this with two piles of quarters, you can put the rows together to make two big rows. This is as good as any "formal" proof, and I sincerely hope it's the kind of proof the teacher shows as an example of a good answer.