An antiPascal triangle is an equilateral triangular array of numbers such that, except for the numbers in the bottom row, each number is the absolute value of the difference of the two numbers immediately below it. For example, the following is an antiPascal triangle with four rows which contains every integer from $1$ to $10$.
\[4\]
\[2 \ \ 6\]
\[5 \ \ 7 \ \ 1 \]
\[8 \ \ 3 \ \ 10 \ \ 9 \]
Does there exist an antiPascal triangle with $2018$ rows which contains every integer from $1$ to $1 + 2 + 3 + \dots + 2018$?
IMO 2018 P3
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