A sum of BDT 200 will be divided among 5 swimmers, named Emran, Durjoy, Chopol, Billal and Anabi, who have just finished a swimming competition. Everyone will receive at least BDT 5 and no two swimmers will receive the same amount of money. Emran has come \(1^{st}\) and will get BDT 80; Durjoy has come \(2^{nd}\), Chopol is \(3^{rd}\), Billal is \(4^{th}\) and Anabi is last. Moreover, the distribution of money is subject to the following conditions: • No one will get any fractional amount of money. • The swimmer who finishes earlier must receive more money than the swimmer(s) he defeats. What are the greatest and least amount of money, consecutively, that Durjoy can receive?

Explanation: Emran comes in \(1^{st}\) and gets 80 . So, the most Durjoy can get is 79 BDT. For the least amount Durjoy can get, he must get more than the remaining 3. To get the least amount for Durjoy, we need to maximize the amount the other 3 can get. This can be done by taking numbers that are close to forming an arithmetic series, since in a series like that, the difference between the amount Anabi can get and the amount Durjoy can get will be the least. Emran takes 80 BDT. That leaves 120 BDT for the remaining 4. So, the required series of numbers will be near to the average of 120 for 4 people, i.e., 30. The series that meets the required conditions is \(32, 31, 30, 27\). Here, the amount Durjoy will get is 32. If we try to decrease this amount then the numbers will be repeated. So, the least amount of money Durjoy can get is 32 .