The Lossless Mistake

Bob buys two things in a shop. With his pocket calculator he calculates in advance what he has to pay: 5.25 dollars. But what he does not notice is that he pressed the division instead of the addition button. At the desk he is not surprised if he hears that he has to pay 5.25 dollars. 

What is the price of the two things Bob has bought?

Know the cost of those 2 things.

For Mistake To Be Lossless...

What was the mistake?

Let's assume that those things costs a and b respectively.

As per Bob's wrong calculation,

a / b = 5.25

a = 5.25 b  ..........(1)

And according to what should have been correct,

a + b = 5.25

Putting (1) in above,

5.25b + b  = 5.25

6.25b = 5.25

b = 0.84

Again putting this value in (1) gives,

a + 0.84 = 5.25

a = 5.25 - 0.84

a = 4.41

 
Hence the cost of 2 things are $4.41 and $0.84.

The Game Of Guesses

In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly.

How many people have guessed three fruits correctly, and how many people have guessed four fruits correctly?

Escape to answer without getting tricked! 

Correct Guesses From The Game Of Guesses

What was the game?

There is absolutely no way that somebody has guessed 3 correctly since if 3 are correct then 4th has to be correct. Hence, nobody guessed 3 correctly.

So number of people with all 4 guess correct is equal to 123 - 43 - 39 - 31 = 10.

10 people guessed all the 4 fruits correctly.

A Mathematical Clue From The Merchant

A rich merchant had collected many gold coins. He did not want anybody to know about them. 

One day, his wife asked, “How many gold coins do we have?”

After pausing a moment, he replied, “Well! If I divide the coins into two unequal numbers, then 32 times the difference between the two numbers equals the difference between the squares of the two numbers.”

The wife looked puzzled. Can you help the merchant’s wife by finding out how many gold coins they have?

Here are mathematical steps to find those!

Using The Mathematical Clue

What was that clue?

Since when divided into 2 unequal numbers difference won't be 0. Let x and y be the 2 unequal numbers.

As per merchant,

32 (x - y) = x^2 - y^2

32 (x - y) = (x - y) (x + y)

Dividing both sides by (x - y) which is non zero as x is not equal to y,

32 = x + y

x + y = 32.

Let's verify with x = 30 and y = 2. So 32 (x - y) = 32 ( 30 - 2) = 896. And x^2 - y^2 = 30^2 - 2^2 = 900 - 4 = 896.

Hence, Merchant had 32 coins in total.

Constructing Magical Square Using Prime Numbers

Whether it’s possible to construct a magic square using the first nine prime numbers (here counting 1 as prime):

1 2 3 5 7 11 13 17 19

Is it?

Find the possibility here!

Impossible Magical Square

What was the task given?

That's impossible task. All the listed prime numbers sums together to 78. For square to be magic, sum of each row & column must be equal. In this case, it should be 78/3 = 26.

For sum of 3 to be even, 1 must be even & other 2 odd (or all even). All 3 odd can't sum even.

In listed prime numbers there is only 1 even number i.e.2. Hence, for other 2 rows/columns we can't have even sum.

An Island Of Puzzles

There is an Island of puzzles where numbers 1 - 9 want to cross the river.

There is a single boat that can take numbers from one side to the other.

However, maximum 3 numbers can go at a time and of course, the boat cannot sail on its own so one number must come back after reaching to another side.

Also, the sum of numbers crossing at a time must be a square number.

You need to plan trips such that minimum trips are needed.

This should be that minimum number! 

Numbers On An Island Of Puzzles

What was the challenge?

We need only 7 trips to send all digits across the river.

1. Send 2, 5, 9 (sum is 16).

2. Bring back the 9.

3. Send 3,4, 9 (sum is 16).

4. Bring back the 9.

5. Now send 1,7,8 (sum is 16).

6. Bring back the 1.

7. And finally send 1,6,9 (sum is 16).

A Door Of Fate Or Logics?

A prisoner is faced with a decision where he must open one of two doors. Behind each door is either a lady or a tiger. They may be both tigers, both ladies or one of each.

If the prisoner opens a door to find a lady he will marry her and if he opens a door to find a tiger he will be eaten alive. Of course, the prisoner would prefer to be married than eaten alive :).

Each of the doors has a statement written on it. The statement on door one says, “In this room there is a lady, and in the other room there is a tiger.”

The statement on door two says, “In one of these rooms there is a lady, and in one of these rooms there is a tiger.”
 
The prisoner is informed that one of the statements is true and one is false.

Which door should the Prisoner open?

This should be his choice!

Logical Choice Of Door

What were the choices?

For a moment, let's assume that first statement is true. The lady is behind the Door 1 and tiger is behind the Door 2. But this makes statement 2 also true where it says there is tiger behind one of these door & lady behind one of these doors. Hence, the statement 1 can't be true.

Hence, statement 2 must be true.

Only possibilities left are -

Door 1 - Tiger
Door 2 - Tiger

Door 1 - Lady
Door 2 - Lady

Door 1 - Tiger
Door 2 - Lady.

Since, the true second statement is suggesting there is lady behind 1 & tiger behind the other door, the possibilities of both tigers or ladies are eliminated.

That's why behind Door 1 is tiger & behind Door 2 is lady.

 

One More CryptArithmatic Problem

What three digits are represented by X, Y, and Z in this addition problem?

  XZY

+XYZ
______
  YZX

Here is the solution!

Solution Of One More CryptArithmatic Problem

What was the problem?

Here is the equation rewritten.

  XZY
+XYZ
______
  YZX
 

Let's start with the tens place. Z + Y = Z is there. That means either Y = 0 or 9 if 1 is carry from ones place.

Since Y is at hundred's place it can't be 0. Hence, Y = 9.

At hundred's column, now we have, X + X = 9. That's only possible if X = 4 and carry 1 forwarded from tens place. So X = 4.

Now, finally, at ones place, we have, 9 + Z = 4. Hence, Z must be 5 with carry 1 being forwarded to the next place.

To sum up, X = 4, Y = 9 and Z = 5.

 

Who Is The Engineer?

On a train, Smith, Robinson, and Jones are the fireman, the brakeman, and the engineer (not necessarily respectively). Also aboard the train are three passengers with the same names, Mr. Smith, Mr. Robinson, and Mr. Jones.

(1) Mr. Robinson is a passenger. He lives in Detroit.
(2) The brakeman lives exactly halfway between Chicago and Detroit.
(3) Mr. Jones is a passenger. He earns exactly $20,000 per year.
(4) The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.
(5) Smith is not a passenger. He beats the fireman in billiards.
(6) The passenger whose name is the same as the brakeman’s lives in Chicago.

Who is the engineer?

Want to know who? Click Here! 

That's Why Smith Is An Engineer!

Would you like to read question first? 

Let's list all the clues once again here.

(1) Mr. Robinson is a passenger. He lives in Detroit.
(2) The brakeman lives exactly halfway between Chicago and Detroit.
(3) Mr. Jones is a passenger. He earns exactly $20,000 per year.
(4) The brakeman’s nearest neighbor, one of the passengers, earns exactly three times as much as the brakeman.
(5) Smith is not a passenger. He beats the fireman in billiards.
(6) The passenger whose name is the same as the brakeman’s lives in Chicago.

Since as per (2), the brakeman lives exactly halfway between Chicago and Detroit, locations Chicago or Detroit can't be nearest to him. Hence, the passenger that (4) is suggesting must be nearer to brakeman than Chicago and Detroit.

Now as per (1), Mr. Robinson lives in Detroit, means he is not the nearest to brakeman. Mr.Jones earning is $20,000/year as per (3), which is not evenly divisible by 3. Hence, the passenger (4) is pointing is not Mr.Jones.

So neither Mr. Robinson not Mr.Jones but Mr.Smith is the nearest neighbor. 

Now Mr. Robinson lives in Detroit and Mr.Smith is living in between Chicago and Detroit but nearer to brakeman. Hence, Mr. Jones must be living in Chicago.

According to (6), Jones must be name of the brakeman as he is sharing his name with the man living in Chicago.

And if Smith is not fireman as per (5), he must be an engineer!   

  

Unique Audiance For A Fairy Tale

A sultan has 14 daughters. He decides to tell every night four of his daughters a fairy tale, but in such a way that every night, there will be another combination of four daughters. How many nights will keep the sultan busy telling fairy tales? 

Find number of nights here!

Nights For Fairy Tales!

Story behind the title?

For a moment, let's name all the daughters as A, B, C, D, E.....N. 

There are 14 x 13 x 12 x 11 = 24024 combinations of daughters. But in these combinations, lots of combinations are repeated. For example, ABCD combination is same as ABDC or DABC etc. There can be 4 x 3 x 2 x 1 = 24 combinations while considering group of 4 daughters here for example it is A, B, C, D. For these 24 combination we should count only 1 as a unique combination.

Hence for 24024 combinations, we have 24024/24 = 1001 unique combination. 

In short, Sultan would be busy for 1001 nights in telling fairy tales to his 14 daughters in unique combinations.

Numbers For The Letters?

A - B = B

B * C = A

D : B = E

C * C = E

C + E = A

For which numbers stand A, B, C, D and E? 

Skip To The Answer!  

Correct Numbers For Letters

What was the question? 

Let's first rewrite all equations and number them

1. A - B = B

2. B * C = A

3. D : B = E

4. C * C = E

5. C + E = A

For which numbers stand A, B, C, D and E? 

From 1, A = 2B. Putting this in 2 gives,

C = 2.

Putting C = 2 in 4 gives, E = 4.

So from 5, A = C + E = 2 + 4 = 6.

Equation 2 gives, B = A/C = 6/2 = 3.

And equation 3 gives D = B * E = 3 * 4 = 12.

Conclusion : A = 6, B = 3, C = 2, D = 12 and E = 4.