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 skilled artist once made a magnificent wax structure made of two wax cubes stacked on top of each other. The height of this structure was equal to the height of the wax cube from which these two cubes were carved out.
He decided to melt the remaining unused wax, mould it into a rectangular block, pack it in a rectangular wooden box and transport it to a warehouse a few miles away. He hired a carpenter to make the box. However, much to the dismay of the artist, the carpenter made a rectangular box that wasn't big enough to pack the unused wax.
The rectangular block of wax he could fit in the box was as tall as the wax structure he had made. Its length was equal to the height of one wax cube in the structure and its breadth was equal to the height of the other cube. How many trips did he have to make to the warehouse?