77. Heat Flow. The temperature of three sides of a square metal sheet is maintained at $0^{\circ} \mathrm{C}$, while the temperature of the fourth side is maintained at $100^{\circ} \mathrm{C}$. Neglecting heat loss due to radiation, find the temperature at the center of the sheet.
77. If four such sheets are superimposed so that each side has one edge at a temperature of $100^{\circ} \mathrm{C}$, then the average temperature of each side will be $25^{\circ} \mathrm{C}^{\star}$. Therefore, the temperature at the center of the sheet is $25^{\circ} \mathrm{C}$.

$$
\text { [L. Moser, M. M., 24, } 273 \text { (May 1951).] }
$$

Generalizing this method, it can be proven that if the sides of a regular metallic $n$-sided polygon are maintained at temperatures of $t_{i}$ degrees, $i=1,2,3, \ldots, n$, then the temperature at the center of this polygon is $\frac{1}{n} \sum_{i=1}^{n} t_{i}$ degrees.