8.1. From 1812 identical squares with a side of 1 mm, a rectangular frame for a group photograph was made (see figure, the boundaries of the photograph coincide with the inner boundaries of the frame). Then the photograph was cut along the lines of the millimeter grid into two rectangular parts. Now two frames were needed, for which 2018 such squares were used. Find the dimensions of the original photograph.

![](https://cdn.mathpix.com/cropped/2024_05_06_63799b39c033d6fb87d1g-1.jpg?height=314&width=488&top_left_y=206&top_left_x=1458)
Answer: $101 \times 803$ (mm).

Solution. Without loss of generality, we can assume that the cut was made vertically. After the cut, two vertical sides of the frame, including the corner squares, were added, which used $2018-1812=206$ squares. Therefore, each side used $206: 2 = 103$ squares, and the same number of squares made up the vertical side of the original frame. Then, the horizontal side of the original frame (excluding the corner squares) was $(1812 - 206) : 2 = 803$ squares. Since the corner squares do not need to be counted, the size of the original photograph is $101 \times 803$ (mm).

Grading Criteria.

"+" A complete and justified solution with the correct answer is provided

" $\pm$ " Instead of the size of the photograph, the correct and justified sizes of the original frame $(103 \times 805$ mm $)$ are found

"干" Partially correct reasoning is provided, but the answer for one or both sides differs from the correct one by 1 mm or 2 mm

"千" Only the correct answer is provided and it is verified that it satisfies the condition

“-" Only the answer is provided

“-" An incorrect solution is provided or it is missing