Invigilator, Students and Exam

A solution to a logical problem where an Invigilator has to make a sitting arrangement plan for some mischeivious students to avoid cheating in an examination. This problem deals with position location for sitting/utilisation where entities/item/students are not in direct contact and are not in a line of sight of each other.

It would be more clear by taking an example. Say, there is an arrangement (a square shaped) of 4x4 benches where 4 students are required to sit for an examination in such a way that no 2 students are sitting horizontally, vertically and diagonally to each other not only adjacently but in line of sight as well.

Now, there are 4 benches each in each of the 4 rows. Say, student A is sitting on 1st Bench of Row 1. So, second student can not sit on any of the benches of Row 1. Also, student B cannot sit on 1st benches of all row and not on 2nd bench of 2nd, 3rd bench of 3rd row and 4th bench of 4th row (because they are in diagonal to 1st bench of 1st row where student A is sitting).

To solve this problem where NxN benches/places are available in Square format and N students/items/entities need to be placed can be solved by placing students/items in such a way that no 2 such students/entities are in line of sight whether it be horizontally, vertically or diagonally.

To get the solution to this problem, choose the Grid size i.e. Square size and see what format/layout should be used.