On Monday, he counts the steps by 3's and has 2 steps left over at the top. On Tuesday, he counts the steps by 4's and has 3 steps left over at the top. On Wednesday, he counts the steps by 5's and has 4 steps left over at the top. On Thursday, he counts the steps by 6's and has 5 steps left over at the top. On Friday, he counts the steps by 7's and has 6 steps left over at the top.
Some areas are inside the closed region, and others are outside of it.
But you can see only the enclosed portion. The rest of the curve is unknown to you. An O marks a spot that is on the outside. The Last Problem of the Week for the year ends with the most famous of mathematical problems. That is, show that there is a 'map' that can be drawn on a torus that needs at least five colors using the rules above.