## permutations n Combinations

There are 10 parking spaces numbered from 101 to 110. At least one car is parked in these slots. If cars can be parked only at the consecutively numbered parking slots, how many such arrangements can be made. Consider that only one car can be parked in one parking slot and all cars are identical.

Check your answer:-

Click here to See SolutionCase 2: now lets say if 2 cars need to be parked in 10 slots, as the cars need to be parked in consecutive slots only, its similar to choosing 1 position out of 9 slots, i.e. 9C1 = 9

if you go on like this, number of ways of parking 10 cars in 10 slots = 1

thus total possible arrangements = 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 +1 = 10*11/2 = 55

## A trip to the beach – Children Cards and their name Puzzle

A mother has twelve children, each born in a different month. They want to go to the beach. She says she’ll take them if they can win a game. She puts the name of each child on a card and tells them she will place the cards face-down in a row on a table in the next room.

She’ll randomly call one child in. The child can turn over cards one at a time, up to half the cards, looking for his or her own name.

If that child finds his or her own name, he or she will be sent outside to play, and won’t be able to communicate with the children still waiting to take a turn. The mother will turn all the cards back face-down, keeping them in the same order, and will randomly call in another child and repeat the process. In order for the children to win the game and go to the beach, all the children must be successful in finding their own names. If any child fails, the game is over, and there will be no trip to the beach! The children can consult each other before their mother starts the game, but those who have already taken a turn cannot contact the others or leave any clues for them.

The children talk among themselves and devise a strategy that all the children will be able to follow perfectly. The game begins, and the first child is called into the room where the game is taking place. A few minutes later, he comes back into the room with the other children, grinning widely. “Pack your swimsuits and your towels!” he says. “We’re going to the beach!”

The child is correct, and knows for certain that the inevitable outcome of the game is that the children will win. How many cards did he turn over before he found his name?

puzzle by Harvey Lerman

## Which number is greater ?

which number is greater ?

99^999 + 1 99^1000 +1

———— OR ———–

99^1000 + 1 99^1001 + 1

Check your answer:-

99^999 + 1 99^1000 +1

A – B = ———— – ———–

99^1000 + 1 99^1001 + 1

=> (99^1001 + 1)*(99^999 +1) – (99^1000 + 1 )*(99^1000 +1)

——————————————————–

(99^1000 + 1 ) * (99^1001 + 1)

Now here we just need to see if the value of the numerator is +v or -ve

lets expand the numerator

99^2000 + 99^1001 + 99^999 + 1 – (99^2000 + 99^1000 + 99^1000 + 1)

=> 99^1001 + 99^999 – 2*99^1000

=> 99^999 ( 99^2 + 1 – 2*99)

clearly it is +ve as 99^2 is much greater than 2*99

thus A is greater than B.

## Which number should replace ? mark

## Let’s see your math quotient

can you tell which number should replace the question mark ?

Check your answer:-

1. (5-5)*2=0 and 0*0=0

2. (11-8)*2=6 and 6*6=36

3. (7-3)*2=8 and 8*8=64 and so

4. (8-2)*2=12 and 12*12=144

soln by **Rajaram C Sah**

## What happened to the missing ten dollars?

Three tourists sought lodging in a small American hotel. The Receptionist

Offered them a three-room suite for $300. The three men went upstairs

With the Hotel Attendant to have a look at the suite. Everything seemed fine, and

Each tourist gave $100 to the Hotel Attendant. When the Receptionist received the

$300 from the Hotel Attendant, he discovered that he had made a mistake: the

Price of the suite was only $250. Therefore, he sent the Hotel Attendant back

With five $10 bills. On his way upstairs, the Hotel Attendant realized it would

Be a problem to distribute the five $10 bills among three people. So he

Slipped two of the $10 bills into his own pocket, and gave back $10 to

Each of the three men. Thus, they had each paid $90, which adds up

to $270. Twenty dollars ended up in the Hotel Attendant’s pocket. Altogether,

That makes $270 + $20 = $290, even though the three guests had originally

Paid $300.

**What happened to the missing ten dollars?**

Click here to See Answer

it should have been

$270 (which they gave) + $30 (which they have) = $300(original money)

OR if you think other way

$250(with hotel) + $20(with waiter) + $30(with tourists) = $300(original money)

## How old is dhoni now?

Dhoni is now two fifth of his older brother’s age and two years from now he will be half of his older brother’s age.

Two years ago, dhoni was only one-fourth the age of his older brother age at that time.

**How old is dhoni now ?**

Check your answer:-

Click here to See Solutionso x = 2y/5;

and

x+2 = (y+2)/2 => 2x +4 = 2+y => 2x – 5x/2 = -2 => x/2 = 2 => x = 4

and

x-2 = (y-2)/4 => 4x – 8 = y-2 => 4x – 5x/2 = 6 => 3x/2 = 6 => x = 4

and y = 10

so dhoni is 4years old now.

## How many oranges were there in the basket ?

You have a basket of Oranges

You gave your mom half of them and half an orange

then, you gave your dad half of whats left & half an orange,

Finally you gave your sister half of whats left & half an orange

and the basket became empty.

**How many oranges were there in the basket ?**

this puzzle is shared by Fun Riddles on puzzless facebook page

Check your answer:-

Now you must be having 3 oranges before you came to your dad(as you gave 1.5 + 0.5 oranges to him)

Similarly you must be having 7 oranges before you came to your mom(as you gave 3.5 + 0.5 oranges to her)