Diagonal across a tiled rectangle
In the figure shown, we have a rectangular grid consisting of 4 vertical square tiles and 8 horizontal square tiles.
A red string is stretched across the grid diagonally as shown in the figure. We see that the number of tiles intersected by the string is 8
What would the number of tiles intersected by the string be if we had a rectangular grid composed of 18 vertical square tiles and 48 horizontal square tiles ?
The answer is 60.
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We note that the an 8x3 group of tiles tessellates the entire 48x18 grid.
The string will make the same pattern against the squares in these 8x3 subgrids as it passes across them, and there are six such subgrids.
Even a crude drawing shows how many tiles are crossed by the string in one subgrid.
Hence the answer, 6*10.