MathDB

An infinite number of squares on an infinitely square grid paper are painted red. Show that you can draw a number of squares on the paper, with sides along the grid lines, such that:
(1) no square in the grid belongs to more than one square (an edge, on the other hand, may belong to more than one square)
(2) each red square is located in one of the squares and the number of red squares in such square is at least

1/5

and at most

4/5

of the number of squares in the square.
[hide=original wording] Ett andligt antal rutor pa ett oandligt rutat papper ar malade roda. Visa att man pa papperet kan rita in ett antal kvadrater, med sidor utefter rutnatets linjer, sadana att : (1) ingen ruta i natet tillhor mer an en kvadrat (en kant kan daremot tillhora mer an en kvadrat), (2) varje rod ruta ligger i nagon av kvadraterna och antalet roda rutor i en sadan kvadratar minst 1/5 och hogst 4/5 av antalet rutor i kvadraten.
[url=http://www.mattetavling.se/wp-content/uploads/2011/01/Final10.pdf]source
PS. I always post the original wording when I doubt about my (using Google) translation.

6

Problems(1)