BdMO National Higher Secondary 2009/1

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Moon
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BdMO National Higher Secondary 2009/1

Unread post by Moon » Sun Feb 06, 2011 11:32 pm

Problem 1:
$300$ politicians are sitting in a room. Each one is corrupted or honest. At least one is honest. Given any two politicians, at least one is corrupt. How many are corrupted and how many are honest?
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Ashfaq Uday
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Re: BdMO National Higher Secondary 2009/1

Unread post by Ashfaq Uday » Tue Oct 18, 2011 11:59 pm

corrupted= 299. honest=1

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samiul_samin
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Re: BdMO National Higher Secondary 2009/1

Unread post by samiul_samin » Tue Feb 20, 2018 9:23 pm

Solution.
At least $1$ politician is honest.Let the honest politician is $H$.
$H$ can be paired up with $299$ politician.But,in every pair we will get a corrupted politician.As,$H$ is not corrupted,all other politicians are corrupted.
So,The number of honest politicians is $\fbox 1$
&the number of corrupted politicians is $\fbox {299}$

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