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
Alan and Bryan meet one Sunday morning to play a game. They sit together at a perfectly circular table with a bag full of perfectly circular coins. The coins are identical. The diameter of the coin is less than that of the table. There is no hole in the table. They have enough coins to cover the entire table. Each player takes turns placing one coin on the table such that no coin touches any other coin or the edge of the table. The game ends when nobody can place a coin. The last one to place a coin wins.
If Alan takes the first turn, who can definitely win the game?