Venn diagram logic question..HELP!
Message posted by RedHead (via 198.81.17.34) on October 27, 2001 at 12:01 AM (ET)

I've gotten seven different answers to this from seven different people. I'm thinking the answer is 10 children. Please Help!!!
How many children are in this family?
Seven wouldn't touch spinach, six wouldn't eat carrots, and five wouldn't eat beans. Four would eat neither spinach nor carrots, three would eat neither spinach nor beans, and two would touch neither carrots nor beans. One of the children wouldn't eat spinach, carrots, or beans. And none would eat all three of the vegetables.

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: Venn diagram logic question..HELP!
Message posted by Tomi (via 154.32.143.90) on October 27, 2001 at 10:07 PM (ET)

To solve the problem, draw three overlapping circles and label them "not Beans", "not Spinach" and "not Carrots".

Now there is one child who likes none - put the number 1 in the very central section where all three circles overlap.

Two will eat neither beans nor carrots. This means that there should be two in the overlap of "not C" and "not B". However you have put a 1 in the very central part, which accounts for one of these, so in the section with only a overlap of "not C" and "not B" you must put the number 1.

Repeating this process for the information that four will eat neither spinach nor carrots and three will eat neither beans nor spinach means you you must put the number 2 in the section with only a overlap of "not S" and "not B" and the number 3 in the section with only a overlap of "not S" and "not C".

Seven won't each spinach. You have already accounted for 2+3+1 children, leaving 1 in the section that is purely "not S". Similarly you are left with 1 in the section that is purely "not C" and 1 in the section that is purely "not B".

Adding up all the numbers in all the sections gives you a total of 10. Hooray!