## Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-) |

# 10-gon game

### #1

Posted 14 July 2013 - 02:34 AM

### #2

Posted 14 July 2013 - 02:15 PM

### #3

Posted 14 July 2013 - 02:24 PM

**Edited by gavinksong, 14 July 2013 - 02:31 PM.**

### #4

Posted 14 July 2013 - 03:18 PM

Spoiler for

remember right angled is not considered acute in the game's directions

### #5

Posted 14 July 2013 - 03:50 PM

Spoiler forremember right angled is not considered acute in the game's directions

**Edited by gavinksong, 14 July 2013 - 03:56 PM.**

### #6

Posted 15 July 2013 - 01:00 PM

remember right angled is not considered acute in the game's directions

I don't see why 90° should be an issue. There are no coins that make 90° -- 10 sides for 360°; angle between any 2 vertices is a multiple of 36° and will never be 90°.

I agree with gavin on the solution.

### #7

Posted 15 July 2013 - 01:13 PM

remember right angled is not considered acute in the game's directions

I don't see why 90° should be an issue. There are no coins that make 90° -- 10 sides for 360°; angle between any 2 vertices is a multiple of 36° and will never be 90°.

I agree with gavin on the solution.

The problem is talking about acute *triangles* (and right triangles and obtuse triangles) formed by three vertices, not angles formed by only two vertices and the center point. I actually got this confused at first too. So any triangle whose base is the diameter of a circle and whose remaining vertex lies on the circle is a right triangle. If you imagine the 10-gon as being circumscribed by a circle, you get a right triangle whenever two of its vertices are opposite each other.

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users