  We present a Hamilton cycle in the $k$-sided pancake network and four
combinatorial algorithms to traverse the cycle. The network's vertices are
coloured permutations $\pi = p_1p_2\cdots p_n$, where each $p_i$ has an
associated colour in $\{0,1,\ldots, k{-}1\}$. There is a directed edge
$(\pi_1,\pi_2)$ if $\pi_2$ can be obtained from $\pi_1$ by a "flip" of length
$j$, which reverses the first $j$ elements and increments their colour modulo
$k$. Our particular cycle is created using a greedy min-flip strategy, and the
average flip length of the edges we use is bounded by a constant.
