Question 71
Some positive integers are written on cards, at least two different numbers on each card. The same number may be written on several cards. Two cards are called *adjacent* if the maximum number on one of them is equal to the minimum number on the other.
Prove that if there are no adjacent cards then all written numbers can be divided into two sets so that any card contains at least one number from every set.
Prove that if there are no adjacent cards then all written numbers can be divided into two sets so that any card contains at least one number from every set.