Zhendarov R.G.

In a bank, there are 2002 employees. All employees came to the anniversary and were seated at one round table. It is known that the salaries of those sitting next to each other differ by 2 or 3 dollars. What is the greatest possible difference between two salaries of the employees of this bank, given that all salaries are different?

#
Between the employees with the highest and lowest salaries, there are no more than 1000 people. Therefore, their salaries differ by no more than 3003 dollars. A difference of exactly 3003 dollars is not possible: in this case, there would be 1000 people on each side of the table, and the salaries of any two adjacent people would differ by exactly three dollars; as a result, the salaries of both neighbors of the employee with the lowest salary would be the same.

A difference of 3002 dollars is possible: the lowest salary is 1000 dollars, and the highest is 4002 dollars, with (in order) employees with salaries of 1002, 1005, 1008, ..., 3996, 3999 on one side, and employees with salaries of $1003,1006, \ldots, 3997,4000$ on the other side.

## Answer

3002 dollars.