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 April 8th, 2014, 02:35 AM #1 Senior Member     Joined: Oct 2013 From: Far far away Posts: 429 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, 12:16 PM #2 Global Moderator   Joined: May 2007 Posts: 6,786 Thanks: 708 Proof is correct.

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