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 Billal can receive?
Explanation: Billal comes \(4^{th}\). So, he must get more than 5 . The least possible value is 6 . Again, \(1^{st}\) position got 80 , leaving 120 for the rest four. To find the greatest value that Bilal can get, the \(5^{th}\) person must get the least amount, that is 5 . The rest 115 is to be distributed among the \(2^{nd}\), \(3^{rd}\) and Bilal. This can be done in two ways. \((40, 38, 37)\) and \((39, 38, 38)\). Since no repetition is allowed, the greatest possible value that Bilal can get is 37 .