Line Plots · Superchallenge problem

A line plot shows how many cookies each of $10$ kids has. Above $1$ there are $2$ X's, above $3$ there are $3$ X's, above $6$ there is $1$ X, above $7$ there are $2$ X's, above $9$ there is $1$ X, and above $10$ there is $1$ X. The kids hand cookies to each other until everyone has the same number. What is the fewest cookies that must be handed from one kid to another?