Question 40
A bulldozer is touring Pascal's triangle. It starts at the top of the triangle, at $\left(\begin{array}{l}0 \\ 0\end{array}\right)=1$. Each move, it travels to an adjacent positive integer, but can never return to a spot it has already visited. Moreover, if it has visited two numbers $a\gt b$, it may not visit $a+b$ or $a-b$. Finally, the bulldozer is confined to the first 140 rows of Pascal's triangle.
Prove that the bulldozer may visit at least 2017 numbers. (By convention, the $n$th row contains the entries $\left(\begin{array}{c}n-1 \\ k\end{array}\right)$ for $k=0, \ldots, n-1$, hence the $n$th row has $n$ entries.)
Prove that the bulldozer may visit at least 2017 numbers. (By convention, the $n$th row contains the entries $\left(\begin{array}{c}n-1 \\ k\end{array}\right)$ for $k=0, \ldots, n-1$, hence the $n$th row has $n$ entries.)