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

## Previous puzzle

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

How many different ways are there to assign the ten decimal digits (0–9) to each face of two cubes to ensure that we can arrange both cubes on any day such that the front faces of the cubes show the current day of the month?

For example, on February 9 the cubes would be placed side by side such that the front face of the cube on the left side shows 0 and that of the one on the right side shows 9.

Two ways of assigning the digits to the faces of the cubes are considered different if and only if it is not possible to get one assignment from the other by performing one or more of the following operrations:

- Rotating (reorienting) the digits with respect to the faces they belong to.
- Rotating the cubes.
- Swapping the cubes.