Leo’s grandma placed five empty plates on a square 1 metre\({}\times{}\)1 metre table for dinner. Show that some two of these plates were less than 75 cm apart.
A square area of size \(100\times 100\) is covered in tiles of size \(1\times 1\) in 4 different colours – white, red, black, and grey. No two tiles of the same colour touch one another, that is share a side or a corner. How many red tiles can there be?