Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?
A game is being played where eight players can last for thirty-five minutes. Six substitutes alternate with each player in this game. Thus, all players are on the pitch for the same amount of time including the substitutes.
A time long back, there lived a king who ruled the great kingdom of Trojan House. As a part of the renovation of the kingdom to meet future security needs, he asked his chief architect to lay down a new play in a manner that all of his 10 castles are connected through five straight walls and each wall must connect four castles together. He also asked the architect that at least one of his castles should be protected with walls. The architect could not come up with any solution that served all of King's choices, but he suggested the best plan that you can see in the picture below. Can you find a better solution to serve the king's demand?
A famous swimmer can swim downstream in a lake in exactly 40 minutes with the lake current.
He can swim upstream in that lake in exactly 60 minutes against the lake current.
The length of the lake is 2 km.
How long he can cover the distance of one side at a still lake with no current?
A couple went on a climbing trip. But only the husband returned from the vacation and said that his wife slipped off while climbing and died. On investigating, the local sheriff arrested him saying, 'Your travel agent called. You murdered your wife.'
The man did not inform anyone about the trip. Then how was the agent so sure that it was a murder?