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.
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
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.