A bag has 20 blue balls and 14 red balls. Each time you randomly take two balls out (Assume each ball in the bag has equal probability of being taken). You do not put these two balls back. Instead, if both balls have the same color, you add a blue ball to the bag; if they have different colors, you add a red color to the bag. Assume that you have an unlimited supply of blue and red balls, if you keep on repeating this process, what will be the color of the last ball left in the bag? What if the bag has 20 blue balls and 13 red balls instead?
7 thieves wanted to lock the treasure looted from a ship. They wanted to put N no. of locks to the treasure where each lock had multiple keys. Find the minimum number of locks N and minimum no. of keys K with every thief subject to the following conditions:-
All the locks should open each time a majority of thieves(4 or more) try to open the locks.
At least one lock remains unopened if less than 4 thieves try opening them.
All locks should have same no. of keys.
All thieves must have same no. of keys with them.
You want to send a valuable object to a friend securely. You have a box which can be fitted with multiple locks, and you have several locks and their corresponding keys. However, your friend does not have any keys to your locks, and if you send a key in an unlocked box, the key [...]
You have three boxes of fruit. One contains just apples, one contains just oranges, and one contains a mixture of both. Each box is labeled — one says “apples,” one says “oranges,” and one says “apples and oranges.” However, it is known that none of the boxes are labeled correctly. How can you label [...]
A farmer returning home from the market must get across the river and return home with his three purchases, a dog, a chicken and a bag of rice. However, He must take them in his boat. He can’t have more than one item with him on his boat at all times. He cannot leave [...]
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