  In this paper we introduce the concept of a space-efficient knot mosaic. That
is, we seek to determine how to create knot mosaics using the least number of
non-blank tiles necessary to depict the knot. This least number is called the
tile number of the knot. We determine strict bounds for the tile number of a
knot in terms of the mosaic number of the knot. In particular, if $t$ is the
tile number of a prime knot with mosaic number $m$, then $5m-8 \leq t \leq
m^2-4$ if $m$ is even and $5m-8 \leq t \leq m^2-8$ if $m$ is odd. We also
determine the tile number of several knots and provide space-efficient knot
mosaics for each of them.
