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A group of six friends discover they have a total of \$21.61 with them on a trip to the movies. Show that one or more of them must have at least \$3.61.

How should I approach this problem? I can see that \$21.61-\$3.61 = \$18.00, which is divisible by $5$ for the remaining friends, but I'm not sure how I'm supposed to show that at least one of them MUST have this amount.

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  • $\begingroup$ hint: $21.61/6=3.601\ldots$ $\endgroup$ – vadim123 May 4 '13 at 22:29
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    $\begingroup$ Another, related hint: If none of them had more than 3.60... $\endgroup$ – Arthur May 4 '13 at 22:30
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If every person had less than 3.61, it would be impossible for the total to be 21.61

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  • $\begingroup$ Ah, I see. Thank you! $\endgroup$ – JesseP_613 May 4 '13 at 22:31
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From what you said you can't show one of them has EXACTLY that amount, only that one must have more. It's a simple argument: If at none of them has 3.61 dollars, then the max that the rest have is 3.60, so the most they can have is: $amount \leq 3.60*6=21.6$

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