## 0.999… = 1 #55

### 0.9999999…….. = 1, true or false?

See Answer

### Proof 1 for 0.999… = 1

`x = 0.999...`

10x = 9.999...

10x - x = 9.999... - 0.999...

9x = 9

x = 1

### Proof 2 for 0.999… = 1

`1/3 = 0.333...`

3x(1/3) = 3x(0.333...) = 0.999...

1 = 0.999...

## Did i speak to Tina or Meena ?

Tina & Meena are twins. One of them lies while the other is truthful. I asked one of them,

**“Does Tina lie?**” “Yes”, was the answer.

**Did I speak to Tina or Meena?**

[Read more…]

## Prisoner and two doors puzzle

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?**

[Read more…]

## 10 digit number #52

### Find the 10 digit number satisfying below conditions

Its first digit is the number of occurrence of 0’s in the number.

Second digit is the number of occurrence of 1’s in the number.

Third digit is the number of occurrence of 2’s in the number.

4^{th} digit is the number of occurrence of 3’s in the number.

and so on up to 10^{th} digit(which is number of occurrence of 9’s in the number).

See Answer

#### Only 10 digit number satisfying these conditions is 6210001000.

## Who did it ?

### Three of these statements are false, so who did it?

**Mr Red:**“Mr Blue did it.”**Mr Blue:**“Mr Red did it.”**Mr Green:**“Mr Blue’s telling the truth.”**Mr Yellow:**“Mr Green’s not lying.”

## What is the next number in series? #50

See Solution

How?

its WELCOME, where each letter is replaced by its sequence number in the english alphabets.

## Poor & Rich

**The poor have it,
rich wants it,
but if you eat,
you will die.
What is it?
**

## What is name of father? #49

IF

Mother’s name is

**Mrs. SIXTY TWO**

Son’s name is

**FIFTY TWO**

Daughter’s name is

**FORTY TWO**

**What is the name of the father?**

Check your answer:-

See Explanation**Mrs.**Sixty two so father’s name should be Sixty two.

## 3 doors, 2 goats and a car

### Problem Statement

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1.

Now the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to switch and pick door No. 2?”

**What should you do? Would you will with your current choice (door no. 1) or should you pick the door no. 2 ?**

See Answer

**But**

Its not right,

**The best strategy to wins the car is to switch every time**as from the below image, if you stay you win one in three times if you switch you win two in three times.

You might still be thinking that there are fifty-fifty chances of winning the game, that is right only when host did not know what was behind the 3rd door, as he knew it already your probability of winning the car will be more when you switch.

Reference: http://www.businessinsider.com/the-most-controversial-math-problems-2013-3#-2

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