Cut 2 equal parts of cake

Given the cake with a irregular piece removed.  How can you cut the cake in two equal parts with one straight line cut of a knife.

Answer:-

Out Of the Box – Cut the cake Horizontally

Cut the cake Horizontally – Two equal pieces- Upper half and Lower Half.

Well, of course the upper half will have the decorations and frosting and all that stuff but please do not consider that.

please leave comments if you have any questions.

How much of a loss did the shopkeeper take?

A lady buys goods worth Rs 200 from a shop, whose shopkeeper is selling the goods with zero profit.

• The lady gives him a Rs 1000 note.      
•  The shopkeeper gets the change from the next shop, keeps Rs 200 for himself, and returns Rs 800 to the lady.
•  Later the shopkeeper of the next shop comes with the Rs 1000 note saying “fake note” and takes his money back.

      How much of a loss did the shopkeeper take?

Answer:-

Rs.1000 LOSS

EXPLANATION -

Transaction 1 (Lady and Shopkeeper 1)

Lady to shopkeeper  =    Rs. 1000(FAKE)                            = Rs 0             (EARN Rs.0)

Shopkeeper to Lady  =    Rs. 200 goods + Rs. 800 change  = Rs.1000    (EARN  –Rs.1000 ) – LOSS

Shopkeeper 2 given and took back Rs1000   –   NO NEED TO CONSIDER

FINALLY-

Shopkeeper 1 loss:     Rs.200 goods+ Rs.800 change – Rs. 1000 fake=  Rs.1000

please leave comments if you have any questions.

How many such operations are necessary to correctly label the boxes?

The first box has two white balls. The second box has two black balls. The third box has a white and a black ball.
Boxes are labeled but all labels are wrong!
You are allowed to open one box, pick one ball at random, see its color and put it back into the box, without seeing the color of the other ball.
How many such operations are necessary to correctly label the boxes?


Answer:-

Just One!
Because we know all labels are wrong.
So the BW box must be either BB or WW. Selecting one ball from BW will let you know which.
And the other two boxes can then be worked out logically.

please leave comments if you have any questions.

1 Ball is defected of 8 can you find in 2 weighs?

There are 8 balls. 7 of them weigh the same. 1 of them has a different weight, (you don’t know if it’s heavier or lighter). How do you find the odd ball with 2 weighs?

Answer:-

Tricky question, Right?

NO, It is not possible.

This can be explained by information theory. We need to extract 16 units of information (A ball may be light or heavy -2 units and it can be one of 8 balls). However, we gain just 3 units of information (light, heavy or equal).

So, we need ceil[log3(16)] = 3 weighing.

In the similar question you linked to,
we had 24 units of information and so we needed ceil[log3(24)] = 3 weighing.

please leave comments if you have any questions.

1 Ball is heavier of of 8 balls, can you find which one?

You have 8 balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. 
 
How can you find the ball that is heavier by using a balance and only two weighing?


Answer:-

Divide the balls into the following groups: (1,2,3),(4,5,6),(7,8)
Step 1.
Weigh (1,2,3) against (4,5,6)
Two possible outcomes:
The two groups are equally heavy. (Case A)
One of these groups is heavier than the other. (Case B)
Case A
Weigh 7 against 8.  Now you have identified the heavier ball in 2 weighing.

Case B
Take the heavier group (assume it to be (1,2,3)), take any two balls and weigh them against each other. Either one of these is heavier else the third ball is.

please leave comments if you have any questions.

Bad King and Wine Bottles puzzle

 A bad king has 1000 bottles of very expensive wine. A neighboring King plots to kill the bad king and sends a servant to poison the wine. Unfortunately the bad king’s guards catch the servant after he has only poisoned one bottle. Alas, the guards don’t know which bottle but know that the poison is so strong that even if diluted 1,000,000 times it would still kill the king. Furthermore, it takes one month to have an effect. The bad king decides he will get some of the prisoners in his vast dungeons to drink the wine. Being a clever bad king he knows he needs to murder no more than 10 prisoners – believing he can fob off such a low death rate – and will still be able to drink the rest of the wine at his anniversary party in 5 weeks time. Explain How ?


Answer:-

Number the bottles 1 to 1000, and write the number in binary format.

bottle 1 = 0000000001
bottle 250 = 0011111010
bottle 1000 = 1111101000

Now take your prisoner’s 1 through 10 and

 Let prisoner 1 take a sip from every bottle that has a 1 in its least significant bit.
Let prisoner 10 take a sip from every bottle with a 1 in its most significant bit. etc.

Prisoner      – 10 9 8 7 6 5 4 3 2 1
Bottle 924  – 1  1  1 0 0 1 1 1 0 0
 
In this, bottle #924 would be sipped by 10,9,8,5,4 and 3

That way if bottle #924 was the poisoned one, only those prisoners would die.
After four weeks,
line the prisoners up in their bit order and read each living prisoner as a 0 bit and each dead prisoner as a 1 bit.
The number that you get is the bottle of wine that was poisoned.

 please leave comments if you have any questions.

Defective stack of coins puzzle

There are 10 stacks of 10 coins each.
Each coin weights 10 gms. However, one stack of coins is defective and each coin in that stack weights only 9 gms.
What is the minimum number of weights you need to take to find which stack is defective? How?

Answer:-

SOLUTION -   1 Measurement Only.

EXPLANATION -

We will take,
1 coin from the first stack,
2 coins from the second,
3 from the third
and
so on.
In total we will have 55 coins.
If all of them were non-defective, they would weigh 550 gms.
If stack 1 is defective, the measure would read 549 gms.
If stack 2 is defective, you will read 548 gms.
and so on.

So by taking one measurement you can identify, which is the defective stack.
please leave comments if you have any questions.