You have a huge box of beautiful decorated tiles, which are enough to provide a border in two rooms. However, you really cant figure out how to arrange them. If a border of two tiles is set all around, there's one left over; if three tiles are set all around, or four, or five, or six, there's still one tile left over. Finally, after trying a block of seven tiles for each corner, it comes out even. What is the smallest number of tiles you could have to get this result?
