April 8th, 2014, 03:35 AM  #1 
Senior Member Joined: Oct 2013 From: Far far away Posts: 431 Thanks: 18  5 investors
Prove that if five investors split a payout of $2 million, at least one investor receives at least $400,000 My attempt: Let the five investors receive a, b, c, d, e as their individual share Then we have 1) a + b + c + d + e = 2,000,000 AND 2)Assume all shares are < 400,000 Therefore a + b + c + d + e < 5(400,000) a + b + c + d + e < 2,000,000 Contradiction Therefore it is false that all shares < $400,000 Which implies that at least one share >= $400,000 Is this correct? Is there a better solution? thanks. 
April 8th, 2014, 01:16 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,852 Thanks: 743 
Proof is correct.
