Question 15
Fill in the grid with the positive integers starting from 1 as shown in the figure, and then use an “L-shaped block” (that is composed of three unit squares which can be rotated or flipped) to frame three numbers and compute their sum. For example, in the figure below, the sum of the three numbers framed by the L-shaped block is $ 10+11+18=39 $. It is known that the sum of the three numbers framed by an L-shaped block is 2019. What is the largest possible value of the largest number among the three numbers framed by an L-shaped block?
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| --- | --- | --- | --- | --- | --- | --- |
| 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| 15 | 16 | 17 | 18 | 19 | 20 | 21 |
| 22 | 23 | 24 | 25 | 26 | 27 | 28 |
| ... | ... | ... | ... | ... | ... | ... |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| --- | --- | --- | --- | --- | --- | --- |
| 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| 15 | 16 | 17 | 18 | 19 | 20 | 21 |
| 22 | 23 | 24 | 25 | 26 | 27 | 28 |
| ... | ... | ... | ... | ... | ... | ... |