EXERCISE $38\mathrm{.}2($Dividing money$)$ Two people have $$10$ to divide between them$-$selves. They use the following procedure. Each person names a number of dollars $($a nonnegative integer$),$ at most equal to $10.$ If the sum of the amounts that the people name is at most $10,$ then each person receives the amount of money she named $($and the remainder is destroyed$).$ If the sum of the amounts that the people name exceeds $10$ and the amounts named are different, then the person who named the smaller amount receives that amount and the other person receives the