A rectangular floor that is 10 feet wide and 17 feet long is tiled with 170 one-foot square tiles. A bug walks from one corner to the opposite corner in a straight line. Including the first and the last tile, how many tiles does the bug visit?
Note that the equation of the diagonal line is \(y=\frac{10}{17}x\) As x goes in integer steps from 0 to 17, y only takes integer values at x=0 and x=17.