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
A gambling game involves a fair die with six faces. Each face is marked with a distinct number of dots from one and six. You pay a fee to play every round of the game. The fee for the first round is ₹0.01. The fee increases by ₹0.01 after each round is played. Thus, the fee to play the second round is ₹0.02, the fee to play the third round is ₹0.03, and so on. Once you have paid the fee, it won't be returned to you.
In each round, after you pay the fee, the die is rolled and you win ₹1.00 times the number of dots that appear on the face facing up. You may quit the game at any moment. How long should you play this game if you want to maximize your profit? What is the profit you expect to make?