# The Billionaire's Bathroom

by Grant Fikes

In two previous puzzles The Billionaire's Gates and The Billionaire's Gates Revisited, we visited a nameless billionaire who built his house on a torus-shaped asteroid and walked through every door exactly once. Well, now he's tired of that house, and he has a new one, which is back on good old Earth. There are still many expensive high-tech gadgets in the house, but this puzzle concerns itself with the floor tiles in the guest bathroom.

There are 100 square tiles of equal size on the bathroom floor, which are arranged in a square pattern. Each tile is either white or black. The black tiles all form one contiguous region; that is, one can draw a path from any black tile to any other black tile without going through any white tiles. However, four black tiles never meet at a single corner; any 2 tile by 2 tile region in the bathroom must have at least one white tile.

You need to use the bathroom. Unfortunately, the billionaire won't let you in unless you can figure out the pattern of black and white tiles on the floor. He hands you this sheet of paper:

The white tiles form ten separate contiguous regions. Each white region is represented by a number in one of that region's squares. The number represents how many white tiles make up that region. For example, the 7 is contained in a region of 7 white tiles.

You really need to use the facilities, so you'd better solve this puzzle as soon as possible. Keeping in mind that the black squares form a single region without any two by two areas, can you figure out the pattern of the floor tiles?