MECHANICAL DEVICES SOLUTION

 
 

 
DEVICE 1 has three hollows and three protrusions
DEVICE 2 has four hollows and three protrusions
DEVICE 3 has three hollows and four protrusions
DEVICE 4 only has four hollows and cannot be moved
 
Device 3 is the only one with four protrusions, so it must fit into device 4 (four hollows)
 
Devices 1 and 2 both have three protrusions, so either will fit into the hollows on the back of device 3, but:
  (a) The back of device 2 has four hollows, so device 1 (three protrusions) won't fit;
  (b) The back of device 1 has three hollows, so device 2 (three protrusions) will fit
 
Therefore device 1 must be inserted into the back of device 3 and device 2 is fitted last
 

HOW TO MANIPULATE THE DEVICES

01) Rotate the energy beam to flow from 3 to 1, then move 3 to the centre
02) Rotate the energy beam to flow from 2 to 4, then move 3 into 4
      Note that the protrusions on 3 must be facing towards 4
03) Rotate the energy beam to flow from 1 to 3, then move 1 to the centre
04) Rotate the energy beam to flow from 2 to 4, then move 1 into the back of 3
      Note that the protrusions on 1 must be facing towards 4 (the back of 3)
05) Rotate the energy beam to flow from 2 to 4, then move 2 to the centre
      Note that initially the protrusions will be facing the wrong way
06) While 2 is in the centre rotate the energy beams to flow from 4 to 2
07) Return 2 to it's original position
      Note that now the protrusions are facing the correct way
08) Rotate the energy beam to flow from 2 to 4, then move 2 into the back of 1