Question 6
A Mathematics test consists of 3 problems, each worth an integral number of marks between 1 and 10 inclusive. Each student scores more than 15 marks, and for any two students, they obtain different numbers of marks for at least one problem. Find the maximum number of students.
Source clarification: The organizer's Traditional Chinese edition explicitly says that the score obtained on each problem is an integer from 1 to 10. This positive-integer score domain is used here; the English wording above is retained.
Submission guidance: Give a full solution, as required for this even-numbered problem by the examination cover.
Source clarification: The organizer's Traditional Chinese edition explicitly says that the score obtained on each problem is an integer from 1 to 10. This positive-integer score domain is used here; the English wording above is retained.
Submission guidance: Give a full solution, as required for this even-numbered problem by the examination cover.