The mechanical octopus is to light up all the glow orbs that forms the 8 corners of a cube. To do that it could use its laser pen and mirrors by passing a continuous beam of photons once through the center of every orb altogether to emit spectra of colors. If it can do it using as few as possible mirrors to light all 16 orbs of a 4x4 square grid, what setup shall the octopus do for the cube orbs?
The 4x4 grid can be lit up with
6 beams, ie 5 mirrors. This can be done multiple ways. Here is one:
Thus we need to find a way of lighting up the cube with the same number of mirrors. My drawing isn't up to it, so I'll try and describe it, referring to the following letters:
First we have a beam through D and then B, extending out slightly past B (it doesn't matter how far). The second beam goes through F, stopping when we are directly below the centre of the cube. The third beam goes through G, stopping when we are level with the top of the cube. We can now go through C and A with the fourth beam. It is now easy to go through the final two (E and H) with two more beams, so we once again needed 6 beams, or 5 mirrors.