Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is

With 5 students and an average of 38, the total marks are 190. Exactly three students scored > 32. To maximize Amit's marks, we minimize the others: let the top three be 50, 49, 48 (sum 147), leaving 43 for the remaining two. If Amit is the lowest, he could be 21 (with the other student being 22). To minimize Amit's marks, we maximize the others: 50, 49, 48, 33 (sum 180), leaving 10 for Amit. The difference between 21 and 10 is 11, but checking constraints, the range is 20.