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We investigate the boundedness of positive solutions of the reciprocalmax-type difference equation  \[ x_{n}=\max\left\{\frac{A_{n-1}^{1}}{x_{n-1}}, \frac{A_{n-1}^{2}}{x_{n-2}},  \ldots, \frac{A_{n-1}^{t}}{x_{n-t}}\right\}, \ \ n=1, 2, \ldots, \]  where, for each value of $i$, the sequence $\{A_{n}^{i}\}_{n=0}^{\infty}$ ofpositive numbers is periodic with period $p_{i}$. We give both sufficientconditions on the $p_{i}$'s for the boundedness of all solutions and sufficientconditions for all solutions to be unbounded. This work essentially complementsthe work by Biddell and Franke, who showed that as long as every positivesolution of our equation is \emph{bounded}, then every positive solution iseventually periodic, thereby leaving open the question as to when solutions arebounded.

On the Boundedness of Positive Solutions of the Reciprocal Max-Type  Difference Equation $x_{n}=\max\left\{\frac{A^{1}_{n-1}}{x_{n-1}},  \frac{A^{2}_{n-1}}{x_{n-2}}, \ldots, \frac{A^{t}_{n-1}}{x_{n-t}}\right\}$  with Periodic Parameters