Problem 44715. 007: Chinese Barrack Invasion

MISSION: Successfully invade a military barrack located in China.

WARNING: There is a row of n security switches protecting the military installation entrance. The switches can be manipulated as follows:

• The rightmost switch may be turned on or off at will.

• Any other switch may be turned on or off only if the switch to its immediate right is on and all the other switches to its right, if any, are off.

• Only one switch may be toggled at a time.

All n security switches are currently turned on. Deactivate the security system by turning off all the switches in the minimum number of moves m (toggling one switch is considered one move.) An alarm will be triggered if more than m moves are made. Quickly, determine the minimum number of moves m .

Be Careful. Do not get caught!!!

HINT: The security system was designed by the Chinese.