  In this paper we examine a procedure that, on starting with an integer $n$,
results in a pair of equal integers that are no greater than $n$. We call the
resulting value the \textit{strange root} of $n$ and we show how this
strange-root-finding procedure is intimately linked to the game of Tchoukaillon
solitaire. We analyze the strange-root-finding procedure in reverse to
determine when a prescribed value is the strange root of at most two integers.
We present a conjecture about strange roots and translate this conjecture into
one involving Tchoukaillon solitaire.
