  We give a short combinatorial proof of the classical pointwise ergodic
theorem for probability measure preserving $\mathbb{Z}$-actions. Our approach
reduces the theorem to a tiling problem: tightly tile each orbit by intervals
with desired averages. This tiling problem is easy to solve for $\mathbb{Z}$
with intervals as tiles. However, it would be interesting to find other classes
of groups and sequences of tiles for which this can be done, since then our
approach would yield a pointwise ergodic theorem for such classes.
