Thread: Discrete math set question someone help?? thank you

In a period of 4 weeks, Joe played tennis every day. He plays at least one set everyday, and played a total of 40 sets. (In each day the nubmer of sets Joe played is an integer.) Show that there is a consecutive span of days during which Joe played exactly 15 sets of tennis.

Originally Posted by peiyilee

In a period of 4 weeks, Joe played tennis every day. He plays at least one set everyday, and played a total of 40 sets. Show that there is a consecutive span of days during which Joe played exactly 15 sets of tennis.

Suppose that is the sum total of all sets completed at the end of the kth day.
Thus . That is a set of 28 different sums.
Construct a new set of 28 different sums, .
Now we have 56 representations of numbers 1 to 55.
Use the pigeonhole principle to conclude.