Question 15
The integers from 1 to 16 have been placed in a $4\times4$ grid paper, as shown in the diagram below. David cuts this grid paper along the thick grid lines to separate the grid paper into two pieces so that the sum of numbers in each piece is exactly $\frac{1+2+3+\cdots+16}{2}=68$. Find as many other solutions as possible that separate this grid paper into two pieces along the grid lines so that the sum of the numbers in each piece is 68. Draw the cutting line on the diagrams provided.
Note that if some regions have common points but do not have any common side, then these regions are not in the same piece. For example, the following way of cutting separates the grid paper into three pieces, even if the sums of the numbers in the shaded part and white part are both 68.
Blank grid (reuse for each drawing):
Note that if some regions have common points but do not have any common side, then these regions are not in the same piece. For example, the following way of cutting separates the grid paper into three pieces, even if the sums of the numbers in the shaded part and white part are both 68.
Blank grid (reuse for each drawing):