  We consider integers whose squares have just three decimal digits. Examples
are e.g. given by $2108436491907081488939581538^2 =
4445504440405440505004450045555054500055550554550445444$ and
$10100000000010401000000000101^2 =
102010000000210100200000110221001000002101002000000010201$. The aim of this
paper is to summarize the current knowledge on squares with three digits,
scattered around webpages and newsgroup postings, and to add a few new
insights. While we will mostly focus on the base $B=10$, several results are
presented for general values of $B$. The used mathematical tools are completely
elementary. However, we give complete proofs of all statements or explicitly
state them as conjectures.
