Question

Consider the following numbers 3, 6, 9, 12, . . . , 75. Show that if we pick 15 arbitrary numbers from them, then we will find two that have sum equal to 81. I understand that there are 12 distinct sets containing pairs that sum to 81 plus a singleton subset {3}. but wouldn't this mean that there are 2 remaining "empty holes" that need to be filled? Not sure how to apply the pigeonhole principle here.

Answer #1

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 16 minutes ago

asked 18 minutes ago

asked 26 minutes ago

asked 33 minutes ago

asked 45 minutes ago

asked 50 minutes ago

asked 57 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago