## 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?

[SOLVED]

## Composite factorial plus one

How many positive integers $$n$$ are there such that $$n! + 1$$ is composite?

[SOLVED]

## Common divisors of sum and difference

There are two numbers that are coprime to each other. What are the possible common positive divisors of their sum and the difference between them?

[SOLVED]