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 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.