Is it possibile ???

Geometry Level 3

9 points so disposed can be connected with the segments as in the figure without detaching the pencil from the paper and you can't do it with more segments. Can you do the same thing if the points are circles with a diameter "d" > 0 with fewer segments? (For point considering the entity of the fundamental geometry that is devoid of any dimension.). The circles don't overlap.

Depends from "d" Yes, 3 No, at least 4 Yes, 2

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1 solution

Dario Bocchi
Nov 28, 2014

d> 0 tells you that circles aren't points. So you can pass also in orher points of the circles that are not the centre( thing that you can't do with points). So you can track segments 3 first from left to right, then from right to left and from left to right again hooked so as to pass through all the circles. Thus, 3 is the correct answer.

I feel the answer should be depends on d. (I got it correct cause my mouse slipped) thats because if d is big enough it would just need 1 1 line to cross all the circles

Julian Poon - 6 years, 6 months ago

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No because if d> 0 on d can certainly find three distinct points aligned and you can draw a segment that unites them: so you can do the same for the other segments

Dario Bocchi - 6 years, 6 months ago

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Yes but this is only true if the circles do not overlap. Maybe you should state that.

Julian Poon - 6 years, 6 months ago

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@Julian Poon Ok thanks i ll put it in the question

Dario Bocchi - 6 years, 6 months ago

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