Question

Suppose the 25 students are seated in a 5 × 5 grid. What is the smallest value of k that guarantees
no student will have the same exam as someone directly to their left, directly to their right, directly
in front of them, or directly behind them?

Answer 1

Suppose the 25 students are seated in a 5 × 5 grid.

Here 2 different versions are enough to manage the 25 students with "someone directly to their left, directly to their right, directly in front of them, or directly behind them"

See the Exam Paper allocation from two sets.

1	2	1	2	1
2	1	2	1	2
1	2	1	2	1
2	1	2	1	2
1	2	1	2	1

Students will be sit like this....

1	2	3	4	5
6	7	8	9	10
11	12	13	14	15
16	17	18	19	20
21	22	23	24	25

So, K = 2.