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Blindfolded Game

There are 4 lights on a device in the direction of north, south, east and west, as shown in the picture. The device can turn 90 degrees clockwise or counterclockwise each time. Now let’s play a game. The player is blindfolded and doesn’t know the initial status of each light (on/off). But he/she can ask the host to change the status of one or more lights each time (by indicating the directions). The host will tell the player how many lights are on after he makes the change, and then he rotates the device clockwise or counterclockwise randomly by 90 degrees (without telling the player). If the player manages to turn on all four lights he/she wins the game. If you are to play this game do you have any strategy to win in finite steps? If not, show your strategy that has the highest probability to win.

asked Nov 1, 2016 by rajaman1994