Leo’s grandma placed five empty plates on a square 1 metre×1 metre table for dinner. Show that some two of these plates were less than 75 cm apart.
A square area of size 100×100 is covered in tiles of size 1×1 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?
One corner square was cut from a chessboard. What is the smallest number of equal triangles that can be cut into this shape?