A $21 \mathrm{~m}$ long, $5 \mathrm{~m}$ wide, and $5 \mathrm{~m}$ high barn has a spider sitting on the centerline of one of its square walls, $1 / 2$ meter from the ceiling. On the centerline of the opposite wall, $1 / 2$ meter from the floor, a fly has been caught in a web. What is the shortest path along which the spider can crawl on the barn wall to reach the fly? Show that the length of this shortest path is not less than 26 m!
The length of the path taken does not change if we imagine cutting the barn along edges that the spider did not cross and laying the uncut edges flat on a plane. It is obvious that the spider crosses the nearest edge first and indeed this gives us the shortest path. Approaching the leg from different sides (Fig. 17), the possible shortest paths in each case are: $26, 25, \sqrt{584}=24 \cdot 16 \ldots$

![](https://cdn.mathpix.com/cropped/2024_05_02_c14e1d35b524114e2251g-1.jpg?height=1306&width=1740&top_left_y=385&top_left_x=149)

Fig. 17

The shortest path is thus achieved when the spider avoids the vertical edges of the barn, crossing one through the ceiling, then descending the side wall to the floor and avoiding the other.

Solved by: Bakonyi Kornélia, Bárány I., Bodonyi J., Fülöp M., ifj. Gacsályi S., Gehér L., Heller L., Horváth M., Hosszú M., Inkovich Gabriella, Izsák I., József P., László F., Lásztity R., Lichtenstein J., Magyar Á. Sz., Magyarosi B., Pál L., Reiner Éva, Silfen P., Sós Vera, Szathmári D., Szuszky O., Tarnóczi T., Turczi Gy., Ungár P., Vörös M.

Only the 25 m path was noticed by: Békefalvi L., Bognár J., Csordás L., Csuhássy Edit, Deák I., Deák K., Erdősy Gy., Farkas J., Kővári T., Lisik E., Mészáros J., Németh R., Ónody J., Párkány M., Serédi B., Spitz Vera, Vékony Mária.