There is a bee and a lizard at the corner of an $l\times b\times h$ cuboid. The bee can fly. The lizard can walk on walls, the ceiling or the floor. Both must reach the diagonally opposite corner.

What is the minimum distance must they cover to do so?

  • $\begingroup$ This sounds like a homework question. $\endgroup$ – SirParselot Sep 10 '15 at 14:17
  • $\begingroup$ @SirParselot No, I already know the answer. $\endgroup$ – ghosts_in_the_code Sep 10 '15 at 14:18
  • $\begingroup$ It wasn't meant to be a jab at you I was just reminiscing in my thoughts of homework long ago. The good old days $\endgroup$ – SirParselot Sep 10 '15 at 14:20

Assuming the "diagonally opposite corner" means "the one on the other side of the center of the room" (that is the internal diagonal). We get:

The bee must travel the length of the internal diagonal which is $\sqrt{l*l + b*b + h*h}$, because it can go in a straight line

And (ah, dagn it, I fell right into that one):

Lizard: let m1, m2, m3 be the sorted l,b,h. Then $\sqrt{(m1+m2)*(m1+m2) + m3*m3})$

  • $\begingroup$ @Geobits This answer is not entirely accurate. Go ahead, post your own answer. $\endgroup$ – ghosts_in_the_code Sep 10 '15 at 14:16
  • $\begingroup$ @ghosts_in_the_code I admit that in my haste I answered too quickly, but seems right now. $\endgroup$ – dmg Sep 10 '15 at 14:20
  • $\begingroup$ The bee answer is correct. I don't know how you arrived at the lizard answer, and it is wrong. $\endgroup$ – ghosts_in_the_code Sep 10 '15 at 14:23
  • $\begingroup$ @ghosts_in_the_code Damn, fell right into that, didn't I? :D $\endgroup$ – dmg Sep 10 '15 at 14:38
  • $\begingroup$ Finally done. . $\endgroup$ – ghosts_in_the_code Sep 10 '15 at 14:42

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