### 10 hard puzzles which will blow your brain out

Dear readers, I have carefully selected the following puzzles from various sources. To enjoy the puzzles you will be required to possess a modest knowledge of mathematics. I can assure you that the puzzles or the brain teasers will simply blow your mind.

You can jump to specific puzzle from the below chapters:-

The incredible December puzzle

One person is standing at the door of his house and another person is walking up and down the pavement. Both of them are counting passers-by for the last one hour. Who counted more and how?

Grandson mentioned an interesting coincidence to his grandfather, in the year 1932 the grandson was as old as the last two digits of his birth year. The grandfather surprised the grandson by saying that the same applies to him also. The grandson thought it was impossible. But the grandfather proved that it is quite possible. How old was each of them in the year 1932?

A man took out the matchsticks from a matchbox and made three heaps on a table. He then said, “There are total 48 matchsticks. If I take as many sticks from the first heap as there are in the second and add them with the second heap, and then take as many from the second as there are in the third and add them with the third, and finally take as many from the third as there are in the first and add them with the first heap, all the three heaps will have same number of matchsticks”. How many matchsticks were there originally in each heap?

The incredible December puzzle

I assume, you know that December is the twelfth month of the year, don’t you? Do you know the meaning of the name? It originates from the Greek word “deka” which means “ten”. So, decalitre means ten litres, decade- ten years etc. I hope you are getting the point. December should have been the tenth month of the year but actually it’s the twelfth. How would you explain this?

One box contains 10 pairs of red and 10 pairs of white socks, another box contains same number of red and white gloves. How many socks and gloves should you take out of the two boxes to select one pair of socks and one pair of gloves of same colour?

A man if runs at a speed of 10 kilometers per hour he will reach a specific spot at 1 p.m. If he runs at a speed of 15 kilometers per hour he will reach the same place at 11 a.m. What should be his running speed to reach the same spot at 12 noon?

There are two factory workers, one is an old man and the other is young. They both live in same place and work at the same factory. It requires the young worker 20 minutes to reach his working place on foot. Whereas the old man takes 30 minutes to walk the same distance. When will the young man see the old man if the old man starts to walk 5 minutes before the young man?

Two clerks are directed to type a report by their employer. The more expert clerk can complete the job in two hours whereas the less expert clerk can do the job in three hours. How should the employer divide the typing work between them such that the entire job can be done as early as possible?

A puzzle expert was asked how old he was. He replied, “add 3 years to my age, multiply it by 3 and then deduct three times my age three years ago, you will know my age”. Can you tell how old he was?

You have two vessels which are marked with measurements. In one vessel you have some acid and in another the same amount of water. Now, to make the chemical solution you pour 20 gm of the acid from the first vessel into the second. After that you pour two-thirds of the solution from the second vessel into the first vessel. Now the first vessel will have four times more fluid than the second vessel. How much acid and water was there?

### Who counted more?

Both of them counted the same number of passers-by. The man who stood at the door counted all those who passed both ways and the one who was walking up and down the pavement counted all the people he met. So, after one hour they would have counted same number of people.

### Grandfather and Grandson

At first it seems that both the grandson and the grandfather are of same age. But there is nothing wrong with the puzzle. Let us see. It is obvious that the grandson was born in the 20th century. Therefore the first two digits of his birth year are 19. The other two digits multiplied by 2 must equal to 32. So, the grandson was born in 1916 and in 1932 he was 16 years old. The grandfather naturally was born in the 19th century. So the first two digits of his birth year is 18. The other two digits multiplied by 2 must equal to 132. So the last two digits will be 66. Therefore the grandfather was born in 1866 and in 1932 he was 66 years old.

### The matchstick puzzle

This puzzle is to be solved from the end. We know that after all transpositions, the number of matchsticks in each heap is same. Since the total number of sticks is 48, it is easy to conclude that after the final step each heap has 16 matchsticks.

Immediately before that we had added to the first heap as many sticks as there were in it, i.e. we had doubled the number. Thus, before that final step there were 8 sticks in the first heap. In the third heap from which we took these 8 sticks had 16 + 8 = 24 sticks.

Now we have the following numbers just before the last transposition:-

First Heap 8

Second Heap 16

Third Heap 24

Further, we know that from the second heap we took as many sticks as there were in the third heap. It means 24 was double the original number. This shows us how many sticks we had in each heap after the second transpositions.

First Heap 8

Second Heap 28

Third Heap 12

It is now clear that before the first transposition i.e. before we took as many sticks from the first heap as there were in the second heap, the number of matchstick in each heap was :-

First Heap 22

Second Heap 14

Third Heap 12

### The incredible December puzzle

Our calendar comes from the early Romans who, before Julius Caesar began the year in March. December was then the tenth month. When the New Year was moved to January 1, the names of the months were also shifted. Hence the difference between meaning of the names of certain months and their sequence.

September (septem means seven) now is the 9th Month

October (octo means eight) now is the 10th month

November (novem means nine) now is the 11th month

December (deka means ten) now is the 12th month

### Socks and gloves

It is enough to take 3 socks because two of them will always be of the same colour. But, it is not so simple with the gloves because they differ not only in colour but also because half of them are for the right hand and the rest for the left hand. So, you must take at least 21 gloves.

### Speed of running

If the man runs at 15 km per hour and was out for two more hours (i.e. as long as if he were running at the speed of 10 km per hour) he would cover an additional distance of 30 km. In one hour we know, he covers 5 km more. So, he would be running for 30 divided by 5 = 6 hours. This determines the duration of his run at 15 km per hour as 6 - 2= 4 hours. Now, it is not hard to find that he covered a distance of 15 X 4 = 60 km. Now, the question is how fast he should run to reach the same spot at 12 noon, i.e. in five hours. So, the answer will be 60 divided by 5 = 12 km per hour.

### Old and young

To reach the factory the old man needs 10 minutes more than the young man. If the old man were to leave home 10 minutes earlier, they would both reach the factory at the same time. Now the old man if leaves home only 5 minutes earlier, the young man would overtake him half-way to the factory, i.e. 10 minutes later (since it takes the young man 20 minutes to cover the entire distance)

### Typing speed

Since the more expert clerk can work 1 and 1/2 times faster than the other, it is clear that his share should be 1 and 1/2 times more than the other so that they can finish the work simultaneously. Hence, the expert clerk should take 3/5 of the work the other should take 2/5 the work. Now, the expert clerk can do the whole job in 2 hours, so, he will do the 3/5 work in 2 X 3/5 = 1 and 1/5 hours or 1 hour and 12 minutes. The other clerk will also finish his job of 2/5 work in the same duration. Thus, the fastest time the two of them can finish the job is 1 hour 12 minutes.

### Age of a puzzle man

Arithmetically, the solution of this puzzle is quite complicated, but it becomes simple when we apply algebra and make an equation. Let us take x for the years. So, his age three years later will be x + 3 and three years ago will be x - 3. We thus have the following equation.

3( x + 3) - 3( x - 3 ) = x

Solving this we obtain that the age of the puzzle expert is 18 years.

### Chemical solution puzzle

Let us suppose that there were x grammes of acid in the first vessel and x grammes of water in the second vessel. After the first operation there remained x - 20 grammes of acid in the first vessel and x + 20 grammes of acid and water in the second vessel. After the second operation there will remain 1/3 ( x + 20 ) grammes of fluid in the second vessel and the amount in the first vessel will be :-

x - 20 + 2/3 ( x + 20 ) = ( 5x - 20 ) / 3

Now, it is said that in the end there was four times as much fluid in the first vessel as in the second, so, we shall have,

4/3 ( x + 20 ) = ( 5x - 20 ) / 3

And we find that x = 100, i.e. there were 100 grammes of fluid in each vessel.

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