A strip of paper consists of 8 squares. Initially, each square contains the number 0. In every move, we choose 4 consecutive squares and add 1 to each of the numbers in those squares. The figure below shows the outcome after several moves. Unfortunately, ink is covering some of the squares. What number is written on this square with a question mark? First, let's call the number of operations with the first 4 squares A, B the second, so on until E, the number of operations with the last 4 squares. The following figure tells us the number of operations that are done on each square. From B and C, we know that A plus B is 30, and A plus B plus C is 42. Thus, we know that C is 12. We know that the difference between F and G is C, which we just found is 12, so G must be 36 minus 12, which is 24, our answer.

strip of paper

consecutive squares

operations

number puzzle

mathematical reasoning