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?
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)
+33614 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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+118608 Thanks Alan, that is really neat. 
I have been thinking about that problems since it was first posted.
+26367 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
+118608 I have added this inot this probability/counting thread.
http://web2.0calc.com/questions/probability-melody#rr0
This thread is also referenced from the "Great answers to learn from" sticky thread
