Question 2
Two infinite rows of evenly-spaced dots are aligned as in the figure below. Arrows point from every dot in the top row to some dot in the lower row in such a way that:
- No two arrows point at the same dot.
- No arrow can extend right or left by more than $1006$ positions.
Show that at most $2012$ dots in the lower row could have no arrow pointing to them.
- No two arrows point at the same dot.
- No arrow can extend right or left by more than $1006$ positions.
Show that at most $2012$ dots in the lower row could have no arrow pointing to them.