Collection Of Puzzles 

1. Four Brothers of Different Heights Stays in a house. The average Height is 74 inches and the difference in height among the first three is 2 inches. The difference between the third and the fourth man is  6inches.

Can you Tell how tall is each Brother ?

3.A family I know has several children. Each boy in this family has as many sisters as brothers but each girl has twice as many brothers each girl has twice as many brothers as sisters

How many brothers and sisters are there?

4. Two identical trains at the equator start traveling round the world in opposite directions . They start together , run at the same speed and are on different tracks .

Which train will wear out its wheel treads fast ?

5. A person  in San Francisco  hired a car to drive over golden Gate Bridge . He started in the afternoon when there was no traffic rush. So he could drive at 40 miles an hour. While returning due to traffic rush he could manage to drive at a speed of 25 miles an hour. 

What was his average speed for the round trip ?

Sol: No, the answer is not 32 1/2 miles an hour , though this figure is the obvious answer . However this represents the average speed of the 2 speeds and not the average speed for whole trip.

If the time is equal to the distance divided by the average speed, then the time for the trip starting from San Francisco equals s/40 and the time for the return trip is s/25 which gives a total time of S/40 + S/25 which is equal to 13S/200.

   Therefore the average speed of the whole trip when average speed equals the distance divided by the time is 2S divided by 13S/200 which equals to 2S times 200/13S , which equals 400/13S or 13 10/13 miles an hour.

6. All the nine digits are arranged here so as to form four square numbers

             9,   81,   324,   576

How would you put them together so as to form a single smallest possible square number and a single largest possible square number?

7. A man who looked like a tourist came to the bicycle shop one day and bought a bicycle for Rs. 350. The cost price of the bicycle was Rs. 300. So my friend was happy that he has made a profit of Rs. 50 on the sale. However at the time of settling the bill , the tourist offered to pay in Travellers cheques  as he has no cash to pay. The bicycle shop owner does not have the facility to encash Travelles cheques at the bank. But he remembered that the shopkeeper next door has such a provision , so he took the cheques to his friend next door and got the cash from him. 

The travellers cheques were all of Rs. 100 each and so he has taken four cheques from the tourist totalling to Rs. 400. On encashing them he paid back the tourist  the balance of Rs. 50.

The tourist happily climbed the bicycle and peddled away whistling a tune .

However , the next morning the shop keeper neighbor who had taken all the travellers cheques to the bank called on him and returned the cheques which had proved valueless and demanded the refund of his money. The shop keeper quietly refunded the money to the neighbor and tried to trace the tourist who had given him the worthless cheques and taken away his bicycle. But the tourist could not be found.

How much did the shopkeeper lose altogether in this unfortunate transaction ? 

Sol: One can think of different solutions for the question, but yet the correct answer is very simple. All we have to consider is that the shop owner could not have possibly lost more than the tourist actually stole.

  The tourist got away with the bicycle which cost the shop owner Rs.300and the Rs.50 change. and therefore, he made off with Rs. 350. And this is the exact amount of the shop keepers loss.

I came to know from the bus company they had only five hundred buses numbered from 1 to 500. From this I was able to deduce the bus number.

Can You tell me the bus Number?

Sol: By experiment we find that the only numbers that can be turned upside down and still read as a number are 0, 1, 6, 8, 9.

The Numbers 0, 1and 8 remain 0, 1 and 8 when turned over, bur 6 becomes 9 and 9 becomes 6. Therefore the possible numbers on the bus were 9, 16, 81, 100, 169 or 196 . However , the number 196 is the only number which becomes a perfect square when turned over because 961 is the perfect square of 31.

    Therefore 196 is the correct answer 

9. We all know that the hour hand and minute hand on a clock ravel at different speeds. However there are certain occasions they are exactly opposite to each other. Can you give a simple formula for calculating the times of these occasions?

Minute past Twelve Y= (30/11)[(n-1)2+1]

where n is the next hour

Lets take the case of at what time between 4 and 5 will the hands be opposite each other ? n=5

   Y= 30x9/11 = 270/11 + 24 6/11

  i.e the hour hand will be 24^6/11  minutes past 4.The formula may be derived from the following :

If X is the distance moved by the minute hand

Y is the distance moved by hour hand

   then X-Y = 30

First time the hands moved around X=12Y

Second time the hands move around X=12Y-10  etc.

10. Some time back while in Delhi I came across a case in a criminal court. A man was being accused of having stolen certain valuable jewels and trying to run away with them, when he was caught by a smart police officer who overtook him.

In cross examination the lawyer for accused asked the police officer how he could catch up with the accused who has already twenty seven steps ahead of him , when he started to run after him "He takes eight steps to five of mine".

       Bur the officer interrogated the lawyer 'How did you ever catch him if that was the case?'

       That's easily explained Sir replied the officer. 'I have got longer stride...two steps of mine are equal to his five.' So the number of steps i required were fewer than his, and this brought to me to the spot where I captured him.'

A member of the jury , who was particularly good at quick caluclations did some checking and figured out the number of steps the police officer must have taken. 

Can you also find out how many steps the officer needed to catch up with the thief?