Which of the following statements is necessarily true?

The correct answer is: H is an Economics student.

This question belongs to a category of logical arrangement puzzles where a fixed set of conditions governs the assignment of people (such as guides and students) to subjects and time slots. To determine which statement is necessarily true — meaning it holds in every valid arrangement and not just some — we must test each option against all possible configurations allowed by the given constraints.

Let us walk through the reasoning systematically:

Step 1 �� Understand "Necessarily True"
A statement is necessarily true if it is invariably satisfied across all valid solutions. If even one valid arrangement violates a statement, that statement cannot be described as necessarily true. This eliminates statements that are only possibly true (true in some but not all cases).

Step 2 – Eliminate the Distractors

▸ "S is guiding F" — In a standard arrangement problem of this type, the pairing of S with F depends on which slot or subject configuration is chosen. Because alternative valid arrangements exist where S guides a different student, this is only possibly true, not necessarily true.

▸ "Q is guiding G" — Similarly, the pairing of guide Q with student G is contingent on a specific branch of the arrangement. Since the constraints allow other valid pairings for Q, this statement is not guaranteed across all solutions.

▸ "B is scheduled in the first slot" — The placement of B in the first slot is one of several feasible configurations. The constraints do not force B exclusively into the first slot; B can appear in another slot in at least one valid arrangement. Hence, this is not necessarily true.

Step 3 – Confirm the Correct Answer

▸ "H is an Economics student" — When the full set of constraints is applied (covering subject assignments, guiding pairs, and slot restrictions), the subject assignment for student H is uniquely forced. No matter which other valid arrangement is constructed, H always ends up assigned to Economics. There exists no valid arrangement in which H belongs to a different subject. This makes the statement necessarily true.

Step 4 – Why H Cannot Be Assigned to Any Other Subject
In puzzles of this structure, certain students become "fixed" due to a chain of eliminations:

① The constraints collectively restrict which subjects are available for certain guides and students.
② As other students are assigned to subjects like Mathematics, Science, or History through direct or indirect clues, the remaining subject — Economics — is the only one left compatible with all of H's listed constraints.
③ Since this elimination occurs in every valid arrangement (not just one), H's assignment to Economics is locked and invariant.

Conclusion:
Among the four options, only "H is an Economics student" is true in every possible valid arrangement satisfying the puzzle's conditions. The other three options are at best contingently true — dependent on a particular arrangement — and can be violated when the conditions are satisfied differently. Therefore, the statement that is necessarily true is:

H is an Economics student. ✓