Question 11
An anti-Pascal pyramid is a finite set of numbers, placed in a triangle-shaped array so that the first row of the array contains one number, the second row contains two numbers, the third row contains three numbers and so on; and, except for the numbers in the bottom row, each number equals the absolute value of the difference of the two numbers below it. For instance, the triangle below is an anti-Pascal pyramid with four rows, in which every integer from 1 to $1+2+3+4=10$ occurs exactly once:
$$
\begin{array}{rrrrrrr} & & &4& & &\\ & &2& &6& &\\ &5& &7& &1&\\8& &3& &10& &9\end{array}
$$
Is it possible to form an anti-Pascal pyramid with 2018 rows, using every integer from 1 to $1+2+\cdots+2018$ exactly once?
Source illustration of the example above:
$$
\begin{array}{rrrrrrr} & & &4& & &\\ & &2& &6& &\\ &5& &7& &1&\\8& &3& &10& &9\end{array}
$$
Is it possible to form an anti-Pascal pyramid with 2018 rows, using every integer from 1 to $1+2+\cdots+2018$ exactly once?
Source illustration of the example above: