Is it possible in a department of 13 persons racked by disse

Solution

Let us name the persons as 1,2....13

If each person is to get along 3 persons

then let us assume 1 with 2,3,4.

Then 2 with 3,4,5

3 with 1,2,4

4 with 1,2,3

Thus 4 persons complete the cycle

Similarly next 5,6,7,8 will form this

and next 9,10,11,12.

13 will be left with no person to get along with.
Hence it is not possible.