The Challenge Ahead of New Manager

In a wood-cutting factory, five large sawing machines stand in a windowless room. Each machine has an on/off switch attached, there being no doubt as to which switch controls which machine.

Outside the door to the room are five back-up on/off switches, one for each machine inside. The power for each machine must first pass through the back-up switch, and then the machine switch before reaching the saw.

The problem is, the new manager cannot decide how these back-up switches match with the machines inside the room. One day, the manager's brother visits. The manager takes him inside the sawing room where all five machines are at work and explains the problem. The brother announces that he intends to leave the room and that when he returns he will be able to match correctly the five switches outside the room to the five machines inside. The brother works alone, cannot see the machines from outside the room and solves the problem purely by operating switches. 

How is it possible?

Read how brother managed to do it! 

Genius Moves by Brother of Manager!

What was the challenge?

Suppose you are the brother of that manager & have accepted the challenge. 

For sake of convenience, we will name switches inside the room operating machines as an 'operating switches' & those which are outside the room as a 'back up switches'.

Though windowless, we assume that operating sound of machine(s) can be heard from outside room but can't see which machine(s) is (are) in operating condition. 

Here is what you should do!

1. Let's label the machines which we are going to keep ON as ACTIVE & others as INACTIVE. 

2. Turn off operating switches of 2 machines so that there are three machine ACTIVE and two are INACTIVE inside the room.

3. Go outside and now your task is to find the 3 back up switches controlling 3 active machines inside the room.

4. You have to switch off three switches in all possible combinations. There are 10 such possible combinations (5C3) of 3 controlling switches out of 5.

5. If 0 represents OFF position and 1 represents ON position then you should try all possible below combination. 

11000
10100
10010
10001
01100
01010
01001
00110
00101
00011

6. There will be exactly one combination in which all three ACTIVE machines  will be OFF & there will be no sound coming out of the room. The three switches having value of 0 are controlling ACTIVE machines while other 2 must be controlling INACTIVE machines.

7. Still we don't know the exact switch operating the each machine. Label 3 switches controlling ACTIVE machines as A, B and C & those controlling INACTIVE machines as D & E. 

Allow some time to cool down all those ACTIVE machines.

8. Now, turn on 2 switches A & B and keep switch E ON. Machines connected to A and B will start working.

9. After a while, turn off the switch B and go inside the room. 

10. The machine which is still operating must be controlled by back up switch A.

11. Touch other 2 which were labelled as ACTIVE & check which has got warmer.

12. The machine which is warmer must be controlled by back up switch B.

13. And since we didn't turn on the switch C (after giving time all to cool down), the machine having normal temperature must be controlled by the switch C.

14. Remember, we had turned off operating switches of INACTIVE machines initially. And before entering into room again we have turned on switch E. 

15. Now, turn on operating switch of one of the INACTIVE labelled machine. 

If the machine starts working it must be connected to the switch E & other to the switch D. And if the machine doesn't start working it must be connected to D & other to E. 

This way, you will find every back up switch located outside the room controlling operating switch of each machine inside the room.

 

Maximize The Chance of White Ball

There are two empty bowls in a room. You have 50 white balls and 50 black balls. After you place the balls in the bowls, a random ball will be picked from a random bowl. Distribute the balls (all of them) into the bowls to maximize the chance of picking a white ball. 

This is the way to maximize the chances!

Way to Maximize White Ball Probability

What was the task given?

Let's distribute 50 black ball in one bowl & other 50 white ball in another bowl.

Then,

Probability (White Ball) = (1/2)(0/50) + (1/2)(50/50) = 0.5.

Now, if 1 white ball is kept in 1 bowl and other 49 white + 50 black = 99 balls in other bowl, then


Probability (White Ball) = (1/2)(1/1) + (1/2)(49/99) = 0.747.

That's nearly equal to 3/4 which is certainly higher than the previous case. And that's the way of maximizing the probability of white ball.

'The Wisest Son'

Once an old called his three sons. He gave them equal money and ask them to buy something that can fill their living room entirely. He told them that he will give all his money and property to the son who is able to do this task as asked.

The first son buys sticks and tries to fill the room but he falls short of sticks. The second son buys straw but he also falls short of filling the room. The third son buys only two things and he is able to fill the room completely and thus earns all the property and money.

What did he buy?

Here is what did he buy! 

Source 

The Wisest Son Deserves Rewards

What was the condition? 

The third son was very wise to choose his option (like you did while choosing to read this blog). There are two/three possible things that he might have bought.

1. He bought a candle & match box. Just ignited that candle in room & light filled in entire room.

2. He just bought perfume & sprayed in room. The smell of perfume occupied the entire room.