Hats Blown Off

Ten people, each wearing his own hat, are crossing a desert when suddenly a gust of wind blows and all the hats were blown off. That time a boy happens to cross nearby and he takes out all the hats and return to them. Now the question is what is the probability of exactly nine hats being returned to the right persons? (i.e) returning the hats to its original owners?


Answer:

The probability is Zero. If exactly 9 hats are returned to them correctly, so must be the 10th hat to the 10th person. It is not a question of probability; or rather, a certainty. There is no mathematics involved here; just a mere commonsense; that's all.

Volume of a Hole

If the earth is digged into a hole of 2 feet length, 2 feet breadth, and 2 feet depth, how much cubic feet of dirt is in the hole?

Answer:

If any one hastens to say it is 8 cubic feet, woebegone for intellectual vacuum! There is no dirt in the hole, as otherwise how can it be called a hole at all?

Sum of First 100 Natural Numbers

If the qustion of sum of first 100 natural numbers is asked most people will readily answer as 5050 using n(n+1)/2 formula. When the same question was asked to Carl Frederick Gauss, the greatest mathematician ever lived, when he was barely 5 years old, he solved it in a most natural and ingenious way for a 5 year old. This method is a basic idea for deriving n(n+1)/2. Can you just imagine how he did it?

Answer:

First he (Gauss) imagined that he had written all the first 100 Natural numbers and started adding in the following way:

1+2+3+4+5+................................97+98+99+100

= (1+100)+(2+99)+(3+98)+(4+97)+..................(50+51)

=101 + 101 + 101 + 101 +.................. 101

= 101 summed 50 times, (because 100 numbers are paired into 50)

= 101 x 50 = 5050.

Truly remarkable for a tender 5 year old to conceive and devise such a marvellous and wonderful method.

100 Vegetables for 100 Dollars

20 Brinjals cost $1; 1 cucumber costs $5; 1 coconut costs $1. You must purchase a combination of all these vegetables, the total number of vegetables should be 100 and also its cost should be $100. (i.e.) make a purchase of 100 vegetables whose cost is also $100.


Answer:

Most people would certainly lament over the fact that 3 unknowns are there but however, only 2 equations could be set-up and hence it cannot be solved. It is better to make an attempt before making any such decision. If we assign the required brinjals, cucumbers and coconuts as x, y, and z then we have

x/20 + 5y + z = 100 ...............(1)

x + y + z = 100 ...............(2)

(2)-(1) gives 19x/20 - 4y = 0.

19x/20 = 4y.

19x = 80y.

x/y = 80/19.

Since 80 and 19 are relatively prime to each other and also x+y+z=100 the least values of x and y should be 80 and 19 and therefore z=1. Hence the soultions are 80 brinjals,19 cucumbers and 1 coconut. Q.E.D.

Mysterious Suicide

An inspector breaks open a room, bolted from inside, finds a body of a man hanging from the ceiling. The dead man is too short a person to do the hanging from the ceiling and there is absolutely no other thing available except some sheet of water on the floor. How could he have committed suicide?


Answer:

'Well', another good puzzle. Have you ever wondered how come the presence of water inside with no containers? If your thinking mill grinds on this score, you could possibly find it out! To cut the long story short, the man committed suicide by climbing over a largepiece of 'ice' and reached the ceiling. After that the ice melted into sheet of water. Got it!!

Convey Message

There are 3 persons, a blind, a deaf, and a dumb respectively. On a certain ill-fated day, the deaf, outrages the modesty of the blindperson's wife and the whole episode was watched by the dumb. He however conveyed the message to the blind person. How could he have done it? The dumb cannot speak or if he manages to pass on the information through sign language, unfortunately, the blind cannot see it. However he succeeded in conveying the message to the blind and the question is how did he accomplish the task?


Answer:

It is a beautiful puzzle because the dumb cannot convey the message orally. If he tried the 'sign language' and did some gestures, the blind cannot 'see' it. What an unfortunate situation!! Yet, the dumb conveyed the news successfully to the blind person. 'Astonishing', well, he conveyed the message to the blind through 'BRAILLE' system.This is the only possible way to have been communicated.

Planting of Roses

If you plant 4 rose saplings in a row and likewise do the same in 5 such rows, how many saplings in total would you have planted in all? Please do not say 20 as answer as it is very trivial one. Is there any other possibility meeting all the criterions?


Answer:

It could also be 10 if the roses are planted in the shape of a star!

The Missing Dollar

Three friends, sharing a single room in a remote sea-side resort, make an advance payment of $10 each. While they are checking out, the owner of the lodging house charges $25 and ask the room-attendant to give back the balance $5 to them. But the dishonest person, pockets $2 himself, and gives back $1 to each one of them. Now every one of the three friends had given $10 originally and gets back $1, thereby incurring an expense of $27. Adding this to $2, pocketed by room-attendant, does not tally with $30. Why? Where does the dollar disappear?


Answer:

Actually the dollar is not missing or lost. Only our thinking mind is 'lost'. Since the $27 contains $25 as rent and $2 as pocketed by room-attendant, where does the question of adding again $2 with $27 and expect it to become $30? Now the following equations will make you more clear: $25(rent) + $2(pocketed amount) + $3 (amount got back) = $ 30 $27(rent+ pocketed amount) + $ 2(pocketed amount) SHOULD NOT = to $30 as we are adding the pocketed amount 2 times. Hence the confusion. Got it?

A mammoth product

What is the value of the product of 26 algebraical expressions (x-a)(x-b)(x-c)...........upto (x-z)where a, b, c, ............ z represent the english alphabets?

Answer:

The answer is more trivial than you think, but more harder than you imagine! Solution: The answer is, just a moment, hold your breath, 0. Youwonder how? Because out of 26 algebraical expressions, (x-x) is also one among them whose vaule is 0. Hence the product is 0.
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Inflation Index(India)



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In this section we want to look at the graph of a quadratic function. The most general form of a quadratic function is,










The graphs of quadratic functions are called parabolas. Here are some examples of parabolas.


Parabolas_Vertex