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April 8th, 2014, 02:35 AM   #1
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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.
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April 8th, 2014, 12:16 PM   #2
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Proof is correct.
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