There are $6$ people in a ship. As the journey is long, they decide to take shifts. In each shift, some wake up and control the ship while others sleep. How many such shifts are required so that for any two persons $A$ and $B$ there exists a shift such that $A$ wakes and $B$ sleeps (minimum)?
I don't know why but I felt that the minimum number of sittings will be when $3$ persons sleep and the other $3$ wake. So I got the following solution :
So the required number of sittings is 4. But I think my solution to be a matter of luck. So my question is
" Is there a mathematical solution to this question?"