Consider a grid unit square with $x$-$y$ plane $0$ to $20$. Draw line $y=\sqrt{2}x$.
How many unit squares in the grid does this line intersect?
And the more general case?
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3This is a variant on a standard problem where you ask the same question for the line from $(0,0)$ to $(a,b$) with $a,b \in \mathbb Z$: see http://math.stackexchange.com/questions/2186274, http://math.stackexchange.com/questions/1151261. In this case, we're connecting $(0,0)$ to $(10\sqrt2, 20)$, which doesn't change things much except that you don't have to worry about passing through any lattice points along the way. – Misha Lavrov Mar 25 '17 at 01:00
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Wouldn't it simply be 20 +20/root 2 rounded up? – fleablood Mar 25 '17 at 01:41