### #1 - Hard Logic Chess Puzzle

Assume you have the white pieces, can you win in a half a move ?

White should grab the rook from a1, place it at d1 and complete the castling move.

Assume you have the white pieces, can you win in a half a move ?

White should grab the rook from a1, place it at d1 and complete the castling move.

It can be easily calculated that the digits 0 to 9 can be arranged into 3628800 distinct ten digit numbers.

But i also knowns how many of these numbers are prime.

Do you ?

Zero

The sum of numbers from zero to nine is 45 and can be divisible by 3 and 9.

I have 100 coins in my wallet.

What is the minimum number of coin(s), i would be required in order to make sure each coin touched exactly three other coins.

4

3 placed flat on the table in a triangle(touching each other) and put the fourth one on top of them in the middle.

Can you convert number zero(0) into a positive number using just one mathematical operator ?

0!

I have mixed 13 decks of cards.

What is the minimum number of cards must be taken out from the above mixed cards to guarantee at least one 'four of a kind'.

13 x 3 + 1 = 40

Explanation:

The number of decks is irrelevant i.e any number of decks can be mixed and still the answer would be same.

Any card drawn will be a Ace,2,3,4,5,6,7,8,9,10,Jack,Queen or King, so there are 13 possibilities each time a card is drawn.

The fastest and luckiest way would need just 4 cards of the same kind.

The slowest way is our solution as it will guarantee a four of a kind.

i.e draw 3 of each kind =>39 cards will be fetched. now next card will guarantee 4 of a kind.

Like an usual car, my new i10 car has 5 wheels(2 front + 2 Rear + 1 spare).

Rear wheel of car will wear out after 21000 kilometers and front wheel will wear out after 29000 kilometers.

What is the maximum distance i can cover assuming changing of wheels is not an issues.

Maximum distance : 30,450 kilometers.

For each 5 kilometers driven using this rotation, each tire will lose (2/29000)+(2/21000) of its tread.So, suppose we drive 5*N kilometers like this. Then, each tire will lose 2*N*((1/29000)+(1/21000)) of its tread. We wish to determine N so that the latter expression gets to be 1, representing all of each tire's tread. That happens when N=6090, which is when 5*N (the total kilometers driven) is 30,450.

I have got three eyes and all are in a straight line.

When my red eye opens, everything freezes.

What Am I ?

A Stoplight

Replace the question mark with the correct number.

4

6*3 equals 18

7*9 equals 63

6*4 equals 24

7*6 equals 42, ? shud b replcd by 4."

Dhoni is now two fith 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 ?

4 years