This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 26

1997 Estonia Team Selection Test, 1
Tags: interval , set
$(a)$ Is it possible to partition the segment $[0,1]$ into two sets $A$ and $B$ and to define a continuous function $f$ such that for every $x\in A \ f(x)$ is in $B$, and for every $x\in B \ f(x)$ is in $A$? $(b)$ The same question with $[0,1]$ replaced by $[0,1).$