Answers to last issue's Brain Teasers

1. Classic puzzle: There is a river. On one side a man is standing with a tiger, a goat and a bunch of grass. The tiger can kill the goat and the goat can eat the grass, when left alone. However, they are all safe when the man is present.
The man has to transport each of them to the other side of the river on a boat. Now the boat can carry one item at a time along with the man. How will he do it and keep them all safe?
Ans: The key to the puzzle lies in realising that the goat is the single object that can both eat and be eaten.
So the man should take the goat first to the other side of the river. The tiger can be left with the grass, since it will not eat it. Then the man should come back and take the tiger across, leaving the grass behind. At this point, if he returns to pick up the grass, the tiger will kill the goat, so the man should take the goat back with him after leaving the tiger.
He should leave the goat behind and take the grass across. Now, the grass can safely be left behind with the tiger, so the man must come back again and fetch the goat. Now all of them have crossed the river safely.
2. Mall puzzle: There is a big shopping mall and it has 4 gates (let's name them as gate A, B, C and D). Every time you come inside the big shopping mall, you have to pay Rs. 5 and every time you leave it, you again have to pay Rs. 5. Also unlike most shopping malls, whatever amount of money you carry with you inside, it doubles! For example if you carry Rs. 5, it will become Rs. 10.
You have to go inside the mall through gate A, come out of B, again go inside through gate C and finally come out of gate D. Now, how much money should you carry inside the mall so that when you finally come out of the gate D, you should be left with no (zero amount) money?
Ans: It is very hard to solve this from guessing. It is easier to solve it using algebra.
We have to find out the correct amount of money you should take inside the mall so that you are left with none. Let the answer be X. We have to reason and find out what the value of X is.
When you enter the mall through gate A, you spend Rs. 5, so the amount becomes (X-5). This amount gets doubled inside the casino and becomes 2(X-5)=2X-10.
Now, when you exit through gate B you will again pay Rs. 5. So the amount which you have now becomes (2X-10-5)=2X-15.
Again, you enter the casino through gate C and spend Rs. 5. The amount (2X-15) gets reduced to (2X-15-5)=2X-20.
Once when you are inside, the amount gets doubled to 2(2X-20)=4X-40.
This time, you will make your final exit through gate D and pay Rs. 5. So this makes the amount (4X-40-5)=(4X-45).
Now, the condition was that after you have completed the task, you should be left with zero money at the end. So, according to this, the remaining amount of money which you have now, i.e, (4X-45), should be equal to 0.
You can verify by calculation that this happens when 4X=45 or X = 45/4=11.25. Hence, you should carry an amount of Rs. 11.25 inside the mall, so that you are left with no money at the end.
3. A few quick ones: 
A. Larry's father has five sons named Ten, Twenty, Thirty, Forty... Guess what would be the name of the fifth?
B. You have 20 apples in a basket. 20 children come to you and each one of them asks for an apple. You want to give an apple to each one of them, but still keep one inside the basket. How will you do it?
C. Name all the numbers from 1 - 100, which have the letter 'A' in their spellings.
Ans: A. Larry B. Give the last child the basket with the apple inside. C. None.