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I feel that this problem is too obvious, this makes me really confused. If someone could just confirm whether I am right or wrong would be awesome.

We consider paths from $(1, 1)$ to $(4, 4)$ in the Cartesian plane. Now check each point having integer coordinates, such as $(2, 3)$ or $(0, 4)$, and color it blue if it lies within $0.95$ units of some point on the path. What is the smallest possible number of blue points one could obtain?

I simply think that you can go from $(1, 1)$ to $(4, 1)$ then up to $(4, 4)$ leaving a total of $7$ blue dots.

Thanks in advance!

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    But is that the *smallest* possible number of blue points? Or are there other paths that would give fewer points? You would need to *prove* that 7 is the smallest possible number of blue points.2011-11-01
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    Hi, thanks for the response. Yeah you are right I do need to prove it, but I wanted a confirmation from someone on my answer.2011-11-01
  • 1
    Maybe you should think of a better name for your question. This one is too vague.2011-11-01

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