### One More CryptArithmatic Problem

What three digits are represented by

XZY

+XYZ

______

YZX

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

+XYZ

______

YZX

**Here is the solution!**Something to tease your brain!

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XZY

+XYZ

______

YZX

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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,

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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

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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!**

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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

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```
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**?