You are playing a probability game with your friend using a fair coin. Both of you decide on a particular sequence that you have to achieve.
Let us suppose you chose the sequence to be: H T H
Your friend chose the sequence to be: H T T
Now you keep tossing coins until you get the sequence and the same is done by your friend. You keep doing that till you achieve your predefined sequence and keep writing the result on paper. At the end of the game the player whose average number of tosses will be lowest, he will win.
The results of the game 1 toss:
You: H T T H T H
Your score: 6
Your friend: H T H H H T H H T T
Your friends' score: 10
The results of the game 2 toss:
You: T T H T T H H T H
Your score: 9
Your friend: T T H H T H T T
Your friends' score: 8
The results of the game 3 toss:
You: T T H H T H
Your score: 6
Your friend: H H T H T T
Your friends' score: 6
Now after 3 games, your average score is 7 and your friend's average score is 8. Now assume that you keep playing the game and play many times. What will be the possible outcome of the following?
In a basket of apples,
when counted in twos, there was one extra
when counted in threes, there were two extra when counted in fours, there were three extra
when counted in fives, there were four extra
when counted in sixes, there was five extra.
However, if the apples were counted in sevens, no extra apple was left. Can you calculate the minimum number of apples that were present in the basket?
A girl was sitting in her hotel room when she heard a knock on the door. She opened the door and found that a man was standing outside. The man said, "Oh! I am really sorry, I thought this was my room." He then walked through the corridor to the elevator. The girl did not know the man. She closed her door and called security asking them to apprehend the man. What made her suspicious of that man? He might have been genuinely mistaken.
