A class of 15 kids visits Paris. 14 kids visit Eiffel Tower, 13 visit Champs Elysees, 12 visit du Louvre and 11 visit la Cite.

[dbranca]

A class of 15 kids visits Paris. 14 kids visit Eiffel Tower, 13 visit Champs Elysees, 12 visit du Louvre and 11 visit la Cite. What is the minimum number of kids that visit all 4 sites.
a) 2
b) 3
c) 4
d) non
Thank you for your help, please point me in the right direction, not sure how to approach the solution

 

[MarkFL]

Hello, and welcome to FMH!

I would set up a table like this:

Child	Eiffel Tower	Champs Elysees	du Louvre	la Cite
1	No	Yes	Yes	Yes
2	Yes	No	Yes	Yes
3	Yes	No	Yes	Yes
4	Yes	Yes	No	Yes
5	Yes	Yes	No	Yes
6	Yes	Yes	No	Yes
7	Yes	Yes	Yes	No
8	Yes	Yes	Yes	No
9	Yes	Yes	Yes	No
10	Yes	Yes	Yes	No
11 ?	Yes	Yes	Yes	Yes
12 ?	Yes	Yes	Yes	Yes
13 ?	Yes	Yes	Yes	Yes
14 ?	Yes	Yes	Yes	Yes
15 ?	Yes	Yes	Yes	Yes

If we make sure no child missed more than one location, we will minimize the number of children who saw all 4 sites. And so I would say this minimum number \(N\) is:

[MATH]N=15-(1+2+3+4)=5[/MATH]

 

[dbranca]

Hello, and welcome to FMH!

I would set up a table like this:

Child	Eiffel Tower	Champs Elysees	du Louvre	la Cite
1	No	Yes	Yes	Yes
2	Yes	No	Yes	Yes
3	Yes	No	Yes	Yes
4	Yes	Yes	No	Yes
5	Yes	Yes	No	Yes
6	Yes	Yes	No	Yes
7	Yes	Yes	Yes	No
8	Yes	Yes	Yes	No
9	Yes	Yes	Yes	No
10	Yes	Yes	Yes	No
11 ?	Yes	Yes	Yes	Yes
12 ?	Yes	Yes	Yes	Yes
13 ?	Yes	Yes	Yes	Yes
14 ?	Yes	Yes	Yes	Yes
15 ?	Yes	Yes	Yes	Yes

If we make sure no child missed more than one location, we will minimize the number of children who saw all 4 sites. And so I would say this minimum number \(N\) is:

[MATH]N=15-(1+2+3+4)=5[/MATH]

Thank you for your reply. I came up with 5 as well, but since 5 is not one of the answer choices I thought my thinking was off.

 

[MarkFL]

Thank you for your reply. I came up with 5 as well, but since 5 is not one of the answer choices I thought my thinking was off.

I was assuming d) meant "none of the above" and so that would be my choice.