I was wondering about MS paint and stumbled upon certain interesting problems. Here they are.

**Problem 1:** Can you draw an equilateral triangle in MS Paint?

**Problem 2:** Can you draw a regular hexagon in MS Paint?

**Problem 3:** Can you draw a regular polygon having odd number of sides in MS Paint?

**Rules:** You cannot use any aid to make measurements of any kind (length or angle). You can only use MS Paint (obviously). You are not supposed to use the co-ordinates to make measurements of any kind (length or angle). However, you can use the co-ordinates for precise placement of your mouse pointer.

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TopNewestIt's impossible; drawing on MS Paint requires the vertices to be lattice points, and it's a well-known result that a regular polygon that is not a square cannot have their vertices on lattice points (using that if \(a,b,c\) are rationals and \(\cos a\pi = b, \sin a\pi = c\), then \(2a\) is an integer).

Of course, assuming that MS Paint's canvas is infinitely divisible (so it's basically a plane of reals times reals), then it's the usual compass and straightedge problem. – Ivan Koswara · 3 years, 6 months ago

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– Adam Zaim · 3 years, 6 months ago

Read my comment below. The equilateral triangle and regular hexagon can be constructed (and should looks okay if the screen resolution and the size of the computer screen is 1:1). Only the pentagon is impossible to construct.Log in to reply

This video shows you how to make a 60 degree angle, an equilateral triangle and a hexagon. Youtube video I hope I didn't break any rules. Plus, constructing a regular pentagon is impossible in Windows XP paint. – Adam Zaim · 3 years, 6 months ago

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I think I got it. picture – Adam Zaim · 3 years, 6 months ago

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– Ryan Soedjak · 3 years, 6 months ago

err how do you draw the circles so precisely?Log in to reply

In Windows 7, you can make a hexagon and a pentagon. Plus, you didn't say a REGULAR hexagon. So, problem 2 and 3 have been solved. But I don't know how to make equilateral triangle. – Adam Zaim · 3 years, 6 months ago

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– Bruce Wayne · 3 years, 6 months ago

Problems 2 and 3 have been revised. Try them out now :PLog in to reply

– Adam Zaim · 3 years, 6 months ago

Heh. I knew it you meant that way. But in Windows 7, I just realized that I can solve those three puzzles easily. Okay, let's say that you do it in Windows XP. I'll try solving these problems. Because I might got it. Might. Hehe.Log in to reply

– Bruce Wayne · 3 years, 6 months ago

Can you provide your Win7 MS Paint solution for the three problems?Log in to reply

After choosing a tool, let's say a pentagon, while holding the shift key, you can make a regular pentagon. That will also work on other tools.

I think making a pentagon in Windows XP paint is impossible. – Adam Zaim · 3 years, 6 months ago

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