  Past observations and simulations predict an increasingly inhomogeneous gas
distribution towards the outskirts of galaxy clusters, but the exact properties
of such gas clumping are not yet well known. The outskirts of Abell 133 benefit
from deep X-ray observations, with a 2.4 Ms ultra-deep Chandra exposure as well
as eight archival Suzaku pointings, making it a unique laboratory to study the
clumping of the intracluster medium. We searched for significant clump
candidates, in particular aiming to identify those that could represent genuine
ICM inhomogeneity. To further understand how clumping biases the thermodynamic
profiles, we compared the measurements including and excluding the clump
candidates. We jointly analyzed Chandra and Suzaku observations of Abell 133.
We selected clump candidates with at least 2$\sigma$ significance based on the
Chandra image and further discussed their origins using information from the
DESI Legacy Imaging Surveys cluster catalogue, as well as the CFHT r-band
image. We performed multiple rounds of Suzaku spectral analysis with different
corrections for the underlying point sources and clump distribution, and
compared the resulting thermodynamic profiles. We detected 16 clump candidates
using Chandra, most of which are identified as background clusters or galaxies
as opposed to intrinsic inhomogeneity. Even after the correction of the
resolved clumps, the entropy profile approaching the outskirts still flattens,
deviating from the power law model expected from self-similar evolution, which
implies that unresolved clumping and other complex physics should contribute to
the entropy flattening in the outskirts.
