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
An island contained chameleons of three different colours: red, green and yellow. The chameleons were studied by some biologists and they found that when two chameleons of different colours met they changed their colours to the third one. They found that there were 2000 red chameleons and 3000 green ones on the day they counted them. They didn't get time to count the number of yellow chameleons.
When the biologists returned to the island 2 years later they found that all chameleons were red in colour. They were certain that no chameleons died because they did not find dead remains of any chameleon. What does it say about the number of yellow chameleons on the day the biologists counted the number of red and green chameleons?