What three digits are represented by

XZY

+XYZ

______

YZX

**X**,**Y**, and**Z**in this addition problem?XZY

+XYZ

______

YZX

**Here is the solution!**
What three digits are represented by **X**, **Y**, and **Z** in this addition problem?

XZY

+XYZ

______

YZX

**Here is the solution!**

XZY

+XYZ

______

YZX

Here is the equation rewritten.

XZY

+XYZ

______

YZX

Let's start with the tens place.

Since

At hundred's column, now we have,

Now, finally, at ones place, we have,

To sum up,

On a train,

(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?

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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

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

So neither

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

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

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!**

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

There are

Hence for 24024 combinations, we have 24024/24 =

In short, Sultan would be busy for

```
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**?

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**.

There are 4 big houses in my home town.

They are made from these materials:**red** marbles,** green** marbles, **white** marbles and **blue** marbles.

***Mrs Jennifer's** house is somewhere to the left of the** green** marbles one and the third one along is **white** marbles.

***Mrs Sharon **owns a** red** marbles house and** Mr Cruz** does not live at
either end, but lives somewhere to the right of the** blue** marbles house.

*** Mr Danny** lives in the **fourth** house, while the first house is not made from **red** marbles.

Who lives where, and what is their house made from ?

**Know about location and home about each!**

They are made from these materials:

*

*

*

Who lives where, and what is their house made from ?

To simplify the process, let's

a.

b. The

c.

d.

e.

f.

g. The

As per clues (b) and (g), 1 and 3 aren't made of

Since 2 is already occupied, as per (d),

According to (a),

The only house left for

To conclude,

A **horse** and a **camel** were carrying **boxes** on their backs. The **horse** started complaining to the **camel** that his load is too **heavy.**

The**camel **replied '*Why are you complaining? If you gave me one of your
boxes I would have ***double** what you have and if I give you one of my
boxes we two would have an **even load.'**

How many boxes do each of the animal (horse & camel) is carrying ?

**Find here the load on each of them!**

The

How many boxes do each of the animal (horse & camel) is carrying ?

As per

C + 1 = 2 (H - 1)

C + 1 = 2H -2

Now in

C - 1 = H + 1

Putting (1) in above,

2H - 3 = H + 2

Again putting this value in (1) gives,

C = 2*5 - 3 = 10 - 3 = 7

In Sahara desert , 3 men found a big** 24L** Jar is full of water. Since
there is shortage of water so they decided to distribute the water among
themselves such that they all have **equal **amounts of it. But they only
have a **13L**, a** 5L** and an **11** liter Jar.

How do they do it?

**Here is how to do it!**

**Source**

How do they do it?

`Replace letters with numbers assuming numbers can't be repeated. `

` `

` `** SEND
+ MORE
----------
= MONEY**

** **

**Process of decryption is here! **

** **

** S E N D
+ M O R E
-----------------
= M O N E Y**

** **

`Now letter M must be representing the carry generated & it must be 1. `

`And if M = 1 then S must be 9 or 8 if carry is generated from hundreds place. `

`In any case, O can be either 0 or 1. But can't be 1 as M = 1 hence O = 0.`

` `

`If O = 0 then E + 0 = N i.e. E = N if there is no carry from tens place. `

`Hence, `**N = E + 1.**

` `

`Let's turn towards tens place now. With no carry from units place N + R = 10 + E .`

`Putting N = E + 1, we get, R = 9. And with carry from units place, we have,`

`1 + N + R = 10 + E, gives us R = 8. Hence either`** R = 9** and** S = 8** or **R = 8** or** S = 9.**

` `

`For a moment, let's assume`** R = 9 **and **S = 8 **with **no carry** from units place, then,

` `

```
8 E N D
+ 1 0 9 E
=========
1 0 N E Y
```

` `

`For this to be correct, we need carry at thousands place generated from hundreds `

`place. That's only possible if E = 9 and carry is generated from tens place`

`forwarded to hundreds place. Since 9 is already being used for R this combination`

`is just impossible.`

` `

`Hence,`** R = 8** and **S = 9** with **carry 1** from units place.

` `

`Now it looks like,`

` `

```
9 E N D
+ 1 0 8 E
========
1 0 N E Y
```

` `

`This means`** D + E >= 10** i.e. **D + E = 10 + Y.** And numbers left are 2,3,4,5,6,7.

` `

IfE = 2then D must be 8 or 9 for D + E >= 10.

`Since 8 and 9 already taken, this is not possible.`

` `

`If`** E = 3** then D can be 7 but Y would be 0 in the case.

`Since O = 0 already taken this value of E is also not valid. `

For any other value of D, D + E < 10 .

` `

`If `**E = 4** then D = 7 or 6 and Y = 0 or 1.

`Both are taken hence this value of E in invalid.`

Also,D <= 5 in the case gives D + E < 10 .

` `

`If`** E = 6, N = 7** then, D <= 5.

`With D = 5 or 4, Y = 0 or 1, both are used for O and M already.`

And for D = 2 or 3,D + E < 10 .

`In short, this value of E is also not valid. `

` `

`So only value of`** E **left is** 5**. Hence,** N = 6 **and** D = 7.** That gives, **Y = 2.**

** **

** **

`To conclude,`

` `

` `**9 5 6 7
+ 1 0 8 5
=========
1 0 6 5 2 **

```
```

You have two **string**s whose only known **property** is that when you light
one end of either string it takes exactly **one hour** to burn. The rate at
which the strings will burn is constant and strings are identical.

How do you measure** 45** minutes?

**That's how to measure 45 minutes!**

How do you measure

1. Burn both the ends of 1st string and 1 end of other string.

2. After 30 minutes, 1st string will be burnt out and half of the other string will be burnt out.So far we have counted 30 minutes.

3. Now burn the other end of 2nd end. It will take 15 minute to burnt out totally. This way, we have counted 30 + 15 = 45 minutes using 2 strings.

After giving each other a friendly hug,

The man wearing a

Based on this conversation, can you find our

Now, the colors left are

To conclude,

Five students - Adam, Cabe, Justin, Michael and Vince appeared for a
competitive exam. There were total five questions asked from them from
which were **two** **multiple choice** **questions (a, b or c)** and **three** were **
true/false** questions. Their answers are given as follows:

**Name** I II III IV V

**Cabe** c b True True False

**Adam** c c True True True

**Justin** a c False True True

**Michael** b a True True False

**Vince** b c True False True

Also, no two students got the same number of correct answers. Can you tell the correct answer? Also, what are their individual score?

Also, no two students got the same number of correct answers. Can you tell the correct answer? Also, what are their individual score?

There are 2 possibilities of scores & that are either

Table 1 |

What we notice here is that, there are few responses to same question by different student matching.

For the

Let's test that apart from Justin who can have score of 4. If any body other scores 4 then he must share at least 3 similar answers with other (excluding Answer III; refer image below). Only Adam has exact 3 matching responses with Justin.

Table 2 |

If Adam's score is 4 (Answers to I, II, IV, V are correct) then, Justin too would score 4 (Answers to II, III, IV,V are correct) since Adam & Justin have same responses to Questions II, IV,V).

If

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