Each of H, U, S, B, A, N and D has an exam on a different day of the same…

Concept

In a seven-position linear schedule, if exactly k people lie between two persons, their position numbers differ by k + 1.

Place the strongest fixed-end condition first, then use the stated gaps and relative-order conditions to fill the remaining positions.

Application

1. Number Monday through Sunday as positions 1 through 7.

2. Only S is after H, so H must be at position 6 and S at position 7.

3. Three people are between B and H, so their position gap is 4. With H at position 6, B is at position 2.

4. Three people are between A and S, so their position gap is 4. With S at position 7, A is at position 3.

5. The remaining positions are 1, 4 and 5. Since N is before D and D is before U, they must be N at 1, D at 4 and U at 5.

Cross-check

The B-H and A-S gaps each contain exactly three people, and the order N-D-U is satisfied. After A are D, U, H and S, giving a count of four.