Investigating Maths Game

• Dec 19th 2006, 04:55 AM
Rachaelb55
Investigating Maths Game
Hi everyone! This is my first post so please bear with me! I have found this site really helpful so far, but I am struggling with a maths investigation and could do with a nudge in the right direction.

The game is:
The six vertices of a hexagon are drawn on a sheet of paper. A move consists of drawing a line between any two of these verticies. Two players take turns in drawing a line, using a different colour. The first player who is forced to form a triangle of his/her own colour is the loser. (onlt triangles whose vertices are amongst the six original vertices count).

I'm looking for strategies that can be used in order to win the game and what happens if I start with a different number of vertices?

I have drawn up a data table to record all of my results so far which include headings of: no. of vertices, no. of lines, no. of possible triangles etc

I have so much to look at I am losing my focus?
Can anyone help???

Many thanks and Seasons Greetings to one and all!
• Dec 19th 2006, 08:45 AM
MathGuru
I played a quick game and this is what it looks like just before any possible additional line will lose (by creating a triangle)

Is this correct?
Notice that there are 6 lines before the losing line.
Is that always the case?

For 3 vertices there would be always 2 lines before the losing line.
For 4 vertices there are either 3 or 4 lines before the losing line depending on how the game progresses.
• Dec 19th 2006, 09:26 AM
F.A.P
Quote:

Originally Posted by Rachaelb55
The first player who is forced to form a triangle of his/her own colour is the loser.

I believe you need some additional moves MathGuru...
• Dec 19th 2006, 09:36 AM
Rachaelb55
Thanks for your reply maths guru but the dreaded loser triangle must be completed by all of one players colour, so although the next move in your diagram would create a triangle it wouldn't necessarily be by the same player (ie all three sides the same colour)
Thanks anyway. What you looked at I also did too!:)
• Dec 22nd 2006, 11:35 AM
MathGuru
Can the same line be drawn by both players?
Can there be a tie?
• Dec 22nd 2006, 01:09 PM
Quick