Can you replace the question mark with the correct number ? 

A convention is held where all the big logicians are summoned. The master places a band on everyone’s forehead. Now all of them can see others’ bands but can’t see his own. Then they are told that there are different colors of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the color of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified. 

The master assures the logicians that the puzzle will not be impossible for anyone of them.

How will the logicians manage ?

Two prisoners ‘Lincoln Burrows’ and ‘Michael Scofield’ are locked in a cell.
There is open window approx 30 feet above the ground of the cell.
They are never able to reach there.

Then they plan to escape by a tunnel and they start digging out.
After digging for more than 20 days, Scofield comes with the different plan and they escaped.

what was the plan ?