There are 5 st and 5 ave. A block is a square of side length 1. There are 26 booths on those streets. Show that there are 2 booths at most 1 mi apart.

Question

In this case, I am assuming that each street and avenue must form a block, so the only case is where the two blocks are adjacent. Therefore, the total distance of the streets and avenues is 7, but there are 26 phone booths. Through pigeonhole, we know that some have to be less than 1 mi apart. Is this answer correct?

Answer 1

As mentioned in the comments, there are 25 corners, where a street meets an avenue. Each booth has a nearest corner (or more than one, if it is exactly halfway between two adjacent corners of the same block), at most half a mile away. Since there are 26 booths, at least two of them must have the same nearest corner.