×

# Doodling with points

$$6$$ points are taken on a plane such that the distance between any two of them is at most $$2$$ units.Show that there are at least two points whose distance is less than $$\sqrt{2}$$.

After you have solved this problem you can use a similar concept for this problem

Post your solution in the comments :)

Note by Eddie The Head
3 years, 5 months ago

Sort by:

I have yet to see an ordering of $$5$$ points that satisfies the above conditions...

As for the proof, I've been trying to make a pigeonhole principle-based proof, but it just isn't working... :| · 3 years, 5 months ago

Perhaps the given statement isn't the tightest possible one? Which then begs the question, how much tighter can you make it?

You can either reduce the number of points, or reduce the minimum distance. Staff · 3 years, 5 months ago

Sir, it would be immensely helpful if you go through the solution that I wrote to one of your problems Click here for the link · 3 years, 5 months ago

You're going in the right direction..... · 3 years, 5 months ago