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
Albert is opening a new library. He wants to keep a special rack of books facing the entrance to give the visitors a glimpse of the kinds of books it has. This special rack can hold only 10 books at a time. Every time a new book arrives at the library, he needs to decide whether to add it to the special rack or just place it in one of the regular racks in the library. A book is removed from this rack only if Albert decides to add a new book to it.
He wants to ensure that at any point in time, each book that has ever arrived at the library will be equally likely to be on the special rack. How is he going to do this?