Logic & Math Puzzle
Difficulty: Medium
There are two rooms A and B which are not connected and whose entrances are closed. Each of the rooms has 5 bulbs inside the room and 10 switches outside the room corresponding to bulbs of both the rooms.
The entrances will stay opened if and only if exactly one of the switches outside A and one of the switches outside B are ON. If both the switches that are turned ON correspond to the same bulb then the bulb will be OFF.
You are asked to find the bulbs corresponding to each of the switches outside rooms A and B. Using optimal methods, find the minimum and maximum number of trials required to complete the task.
Note: A trial is defined as turning one of the switches outside A and one of the switches outside B ON and checking the bulbs in the rooms A and B. There is no way to find which bulbs are ON from outside the rooms. The bulbs are at a reasonable height so that you can’t touch any of them.
Bonus:Assume that you are choosing both the switches(one from A and one from B) randomly i.e., not using optimal methods, find the probability that the task is completed in minimum number of trials.
Comments/Solutions are Welcome.
PS: I will be giving one puzzle everyday from today. Enjoy solving the puzzles.
