Build study pairs that help each other

A useful study pair can help in both directions: one student has stronger Maths marks, while the other has stronger Physics marks. This is different from pairing the highest scorer with the lowest scorer so that help goes mostly one way. Define the goal before choosing the method.

To reduce the search, first group students into total bands. We use 150–174, 175–199, 200–224, 225–249, 250–274 and 275–299. The endpoints do not overlap: 250 belongs to 250–274. The counts in these six bands are 2, 6, 9, 6, 5 and 2. Equal widths do not create equal numbers of students.

Check the two students against each other #

for each total band B:
    M = students in B with Mathematics > Physics
    P = students in B with Physics > Mathematics
    for each student X in M:
        for each student Y in P:
            if X.Mathematics > Y.Mathematics AND Y.Physics > X.Physics:
                report a candidate study pair

The two personal-strength groups are a shortcut to candidate generation. We still check X’s Maths against Y’s Maths and Y’s Physics against X’s Physics. A student with equal marks in both subjects goes into neither strict group. This does not mean they cannot have any useful partner.

With groups of a and b students, there are a × b cross-group candidate checks, not (a+b) squared. An 8-student group split into 4 and 4 needs 16 cross-group checks; all distinct unordered pairs among 8 would be 28. The complete walkthrough lists candidate pairs, so one student may appear more than once. It does not allocate exclusive teams.