(a) A stadium has 35 rows of chairs, each row has exactly 5 seats labeled A, B, C, D, E. In each seat there is either a child or an adult. Prove that there are at least two rows with the same seating arrangement (ex. child, adult, child, child, adult).
(b) You have 3 buckets, the first of size 4 gallons, the second of size 10 gallons and the third of size 15 gallons. Show that using these 3 buckets you can measure any number of gallons over 22 gallons. For example, you can make 24 gallons using 6 refills of the first bucket.