Ruth has two decks of 160 cards; one deck is red and the other deck is blue. Each deck has the numbers 1 to 160 written on the cards, one number per card. Ruth shuffles each deck and deals it out into sixteen stacks each containing 10 cards. This gives her 32 stacks of 10 cards each-16 red stacks and 16 blue stacks. She then tries to arrange them into 16 stacks of 20 cards each (10 red, 10 blue) by placing cach red stack on a blue stack, in such a way that each of the new stacks contains a red card and a blue card with the same number. Use Hall's Theorem to show that Ruth can always do this.