Question

There are n sheep relaxing in a field. They are positioned at points with integer coordinates. Each sheep has a square sunshade, so as not to overheat. The sunshade of a sheep standing at position (x, y) spreads out to a distance of d from (x, y), covering a square whose middle is at (x, y) and whose sides are of length 2d. More precisely, it covers a square with vertices in points (x d, y d), (x d, y + d), (x + d, y
d.And (x + d, y + d). Sheep are in the centres of their sunshades. Sunshades edges are parallel to the coordinate axes. Every sheep spreads out its sunshade to the same width. No two sunshades can overlap, but their borders can touch. What is the maximum integer width d to which the sheep can spread out their sunshades?

Answer 1

here are n sheep unwinding in a field. They are situated at focuses with number directions. Every sheep has a square sunshade, so as not to overheat. The sunshade of a sheep remaining at position (x, y) spreads out to a separation of d from (x, y), covering a square whose center is at (x, y) and whose sides are of length 2d. All the more definitely, it covers a square with vertices in focuses (x d, y d), (x d, y + d), (x + d, y d.And (x + d, y + d). Sheep are in the focuses of their sunshades. Sunshades edges are parallel to the arrange tomahawks. Each sheep spreads out its sunshade to a similar width. No two sunshades can cover, however their fringes can contact. The most extreme whole number width d to which the sheep can spread out their sunshades is zero.

The solution is given in the following image.