A spider stands on one corner of a solid wooden cube. On the opposite corner sits a delicious fly. The spider can scurry across the cube’s surface at a speed of 3 inches per
second. The fly needs 10 seconds before he can fly away.
What is the smallest cube for which the fly can escape in time?
The shortest path from (0,0,0) to (x,x,x) is to consider the x by 2x rectangle obtained by "unfolding" the cube. The distance is √5*x.
√5*x inches = (3 inches/sec) * 10 sec
x = 30/√5 = approx. 13.416 inches is the breakeven side length for the cube. So if the cube is slightly larger than that, the fly can escape.

Posted by Larry
on 20240805 08:53:39 