more problems
Ok, so I am impressed at the problem solving ability of 2+2. So now I want to see if there are any problems I know that 2+2'ers can't solve in 5 minutes.
Some starters:
(A) Show that given a sphere and any five points on the surface of that sphere, there exists a closed hemisphere that contains four of them.
(B) Show that any continuous map f : B^n \to B^n has a fixed point; ie there exists p \in B^n such that f(p) = p. Here B^n denotes the Euclidean ball of radius B.
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