2
$\begingroup$

Question: Suppose you have a circle with equal numbers of 0’s and 1’s on it’s boundary, there is some point I can start at such that if and travel clockwise around the boundary from that point, I will never see more 1’s than 0’s.

Where I am at: I know since there are equal numbers of 0’s and 1’s there must be an even number of points on the boundary. that is k = 2j, for some j integer.

Where I get Stuck: I dont understand how to use induction to show there will never be more 1s than 0s.

$\endgroup$
2
  • 1
    $\begingroup$ Hint: with a fixed orientation on your circle, find a $1$ that is immediately followed by a $0$, remove them both, and use the induction hypothesis with the same orientation. $\endgroup$
    – Aphelli
    Commented Aug 7, 2019 at 8:09
  • $\begingroup$ @Mindlack just wondering why does it have to be a 1 followed by a 0 and not another pair? $\endgroup$
    – learning_maniac
    Commented Dec 3, 2019 at 2:25

0

Reset to default

You must log in to answer this question.