3. At a 12-week conference in mathematics, Sharon met seven of her friends from college.During the conference she met each friend at lunch 35 times, every pair of them 16 times, everytrio eight times, every foursome four times, each set of five twice, and each set of six once, butnever all seven at once. If she had lunch every day during the 84 days of the conference, did sheever have lunch alone?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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3. At a 12-week conference in mathematics, Sharon met seven of her friends from college.
During the conference she met each friend at lunch 35 times, every pair of them 16 times, every
trio eight times, every foursome four times, each set of five twice, and each set of six once, but
never all seven at once. If she had lunch every day during the 84 days of the conference, did she
ever have lunch alone?

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