  For a one-dimensional simple symmetric random walk $(S_n)$, an edge $x$
(between points $x-1$ and $x$) is called a favorite edge at time $n$ if its
local time at $n$ achieves the maximum among all edges. In this paper, we show
that with probability 1 three favorite edges occurs infinitely often. Our work
is inspired by T\'{o}th and Werner [Combin. Probab. Comput. {\bf 6} (1997)
359-369], and Ding and Shen [Ann. Probab. {\bf 46} (2018) 2545-2561], disproves
a conjecture mentioned in Remark 1 on page 368 of T\'{o}th and Werner [Combin.
Probab. Comput. {\bf 6} (1997) 359-369].
