Question 33
On the blackboard there is written a 17-digit number made up of only 1 and 2. Paolo enters and rewrites the number in reverse sequence, aligning it under the previous one. Gianni enters and writes under each column the maximum figure that appears in that column. Alberto enters and writes under each column the minimum figure that appears in that column, then deletes the first two lines. Carla enters and finds the numbers 12212212221221221 and 11211111211111211 written and it is explained to her what Paolo, Gianni and Alberto did. How many different numbers could be written on the blackboard as the first number?