Question 113
Consider the following grid board in which all natural numbers were written diagonally.
| $\ddots$ | | | | | |
| :---: | :---: | :---: | :---: | :---: | :---: |
| 10 | $\ddots$ | | | | |
| 6 | 9 | $\ddots$ | | | |
| 3 | 5 | 8 | 12 | $\ddots$ | |
| 1 | 2 | 4 | 7 | 11 | $\ddots$ |
Each small square has a position denoted by $(x, y)$, where $x$ is the column, counted from left to right, and $y$ is the row, counted from bottom to top. For example, 12 is the number written in the square at position $(4,2)$:
a) Determine the number in the square at position $(4,4)$.
b) Determine the number in the square at position $(1,2016)$.
c) Determine the number in the square at position $(2013,2017)$.
| $\ddots$ | | | | | |
| :---: | :---: | :---: | :---: | :---: | :---: |
| 10 | $\ddots$ | | | | |
| 6 | 9 | $\ddots$ | | | |
| 3 | 5 | 8 | 12 | $\ddots$ | |
| 1 | 2 | 4 | 7 | 11 | $\ddots$ |
Each small square has a position denoted by $(x, y)$, where $x$ is the column, counted from left to right, and $y$ is the row, counted from bottom to top. For example, 12 is the number written in the square at position $(4,2)$:
a) Determine the number in the square at position $(4,4)$.
b) Determine the number in the square at position $(1,2016)$.
c) Determine the number in the square at position $(2013,2017)$.