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Question: 2014 Fall Midterm - 6

Author: Michiel Smid

Consider a square with sides of length 3. Assume this square contains 10 points. Which of the following is true?

a) At least two of these $n$ points are at distance at most $1$

b) At least two of these $n$ points are at distance at most $\left. 1 \middle/ \sqrt{2} \right.$

c) At least two of these $n$ points are at distance at most $\sqrt{2}$

d) None of the above

Consider a square with sides of length 3. Assume this square contains 10 points. Which of the following is true?
(a)
At least two of these $n$ points are at distance at most $\left. 1 \middle/ \sqrt{2} \right.$.
(b)
None of the above.
(c)
At least two of these $n$ points are at distance at most $1$.
(d)
At least two of these $n$ points are at distance at most $\sqrt{2}$.