How can you construct a plane where every point is coloured either black or white such that two points of the same colour are never a unit distance apart?
Puzzle of the week
Alex and Bob work as financial advisors for the same company. They draw equal salaries from the company. They behave well at the office. Both work on similar assignments. Each assignment requires a yes-no decision. The company uses the decisions made by them to make profits.
After the recession hit the company very badly, one of them has to be fired. Both Alex and Bob have worked on almost the same number of assignments in the last ten years. Alex has been consistently taking about 80% decisions correctly every year. Bob, on the other hand, has been taking only about 5% correct decisions every year.
Assuming that the performances of Alex and Bob would remain the same in future, who should the company fire to maximize its profits in the years to come? Why?
Random puzzle from the past
There are 100 pirates on a ship. They have distinct dates of birth. They find 1000 gold coins. They want to distribute the coins among themselves. The oldest pirate is supposed to propose a distribution of the coins, and then all the pirates, including himself, vote on whether the distribution is acceptable. If at least half of the pirates on the ship vote for it, the coins are distributed according to the proposed distribution. Otherwise, the oldest pirate who proposed the distribution is killed and thrown overboard, and the oldest among the remaining pirates makes a new proposal. This continues until a proposal is accepted.
Each pirate decides his vote after considering three factors. For each pirate, survival is the most important necessity. After ensuring survival, each pirate maximizes the number of coins he gets. He prefers to throw the oldest pirate overboard if it doesn't affect his survival and the maximum number of coins he gets.
Which pirate gets the greatest number of gold coins? How many coins does he get?