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# I think this is a 'mutually exclusive' question...

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100 people, 85 carry a phone, 80 carry a beeper, 75 speak 2 languages, 70 wear suits.  What is the minimum number of people who must have all of the above?

Guest Jun 13, 2015

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with Alan's pictorial representation:

void red (suits) = 100 - 70

void blue (language) = 100 - 75

void green (beeper) = 100 - 80

void black (phone) = 100 - 85

100 - (100-70) - (100-75) - (100-80) - (100 -85) = 100 - 30 - 25 - 20 - 15 = 10

heureka  Jun 15, 2015
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70 suit wearers - 25 unable to speak two languages - 20 with no beepers - 15 with no phone = 10 (minimum number of people who have all four)

Guest Jun 13, 2015
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Here's a pictorial representation.  The dotted lines enclose the overlap of all four criteria and cover 10 people (from 25 to 35 on the diagram).

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Alan  Jun 15, 2015
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Thanks Alan, that is really neat.

I have been thinking about that problems since it was first posted.

Melody  Jun 15, 2015
#4
+18827
+10

with Alan's pictorial representation:

void red (suits) = 100 - 70

void blue (language) = 100 - 75

void green (beeper) = 100 - 80

void black (phone) = 100 - 85

100 - (100-70) - (100-75) - (100-80) - (100 -85) = 100 - 30 - 25 - 20 - 15 = 10

heureka  Jun 15, 2015
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