# Fun with MS Paint

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. Note by Bruce Wayne
6 years, 6 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

It'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.

- 6 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.

- 6 years, 6 months ago

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.

- 6 years, 6 months ago

Problems 2 and 3 have been revised. Try them out now :P

- 6 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.

- 6 years, 6 months ago

Can you provide your Win7 MS Paint solution for the three problems?

- 6 years, 6 months ago

In windows 7, there are three tools. You can make a triangle, a hexagon and a pentagon by using these tools.

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.

- 6 years, 6 months ago

I think I got it. picture

- 6 years, 6 months ago

err how do you draw the circles so precisely?

- 6 years, 6 months ago

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.

- 6 years, 6 months ago