Inspired by Chester Robinson - Part 2

Geometry Level 4

What is the least number of circular arcs needed to cover all 16 spots if you were using a pen and it could not be removed from the page?

Treat the spots as a 0-dimensional object. They do not have length or width.
Treat the circular arcs as a 1-dimensional object. They do not have width. Each arc is the arc of a circle of fixed radius. You cannot simply use a curved line.

Inspiration

7 4 3 6 5

Calvin Lin by Calvin Lin

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Pranjal Jain
Feb 17, 2015

The 3 concentric circles may be drawn with centre at centre of diagram. Smallest one will cover innermost 4 dots, largest will cover 4 corners and medium one will cover remaining 8 dots.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Your solution does not meet the requirement that "pen could not be removed from the page".

Calvin Lin Staff - 6 years, 3 months ago

Log in to reply

It would gonna be interesting then. I'll keep on thinking.

Pranjal Jain - 6 years, 3 months ago

[I thought the person who posted a solution was the poster of the question. As such, this comment is not relevant.]

Exactly. There shouldn't have been the requirement of not removing one's pen. And technically speaking, can a whole circle be considered an arc?

Olawale Olayemi - 6 years, 3 months ago

Log in to reply

Yes, a whole circle can be considered an arc. However, since these circles are not tangential, we cannot draw then without lifting our pen. So, in this solution, he actually needs 5 arcs. The 3 that were stated + 2 arcs that will help us to connect up these circles.

Why shouldn't there be that requirement? I placed it there because I wanted it to. I could add whatever requirements I want, which may/would affect the answer.

As it turns out, the answer for the wider scenario where we are allowed to lift our pen, is still the same. Relaxing this constraint does not allow us to improve on the bound.

Calvin Lin Staff - 6 years, 3 months ago

Log in to reply

@Calvin Lin – I thought the person who posted a solution was the poster of the question. That's why I said there shouldn't have been that requirement if his answer is to be correct

Olawale Olayemi - 6 years, 3 months ago

Log in to reply

@Olawale Olayemi – Ah, your comment makes sense in this context. Thanks! I edited your first comment to reflect this.

Calvin Lin Staff - 6 years, 3 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...