•There are 196 control panels lined up in a row along a long warehouse.
Each control panels has its own switch and is currently switched off.
•The room has an entry door and an exit door.
There are 196 engineers lined up outside the entry door.
Each control panel is numbered consecutively from 1 to 196.
So is each Engineer.
1 enters the room, switches on every control panel, and exits.
2 enters and flips the switch on every second control panel (turning off control panels 2, 4, 6, …).
3 enters and flips the switch on every third control panel (changing the state on control panels 3, 6, 9, …).
This continues until all 196 engineers have passed through the room.
•What is the final state of control panel No.
•How many of the control panels are left working after the 196th Engineer has passed through the room?