The following is called the Chaos Game. Start with a square ABCD in which A is located at (0, 0), B is
located at (27, 0), C is located at (27, 27), and D is located at (0, 27). Then, roll a fair die. We will say
that A is the winner if we roll a 1, B is the winner if we roll a 2, C is the winner if we roll a 3, and D is
the winner if we roll a 4. If we roll a 5 or 6, we disregard the roll and roll again. Each roll of the die generates a point inside or on the boundary of the square according to the following rules.
Start: Roll the die. Mark the winning vertex and call it P1.
Step 1: Roll the die again. From P1 move two-thirds of the way straight towards the next
winning vertex. Mark this point and call it P2.
Steps 2, 3, etc.: Continue rolling the die, each time moving to a point two-thirds of the way
from the last position to the winning vertex.
The grid below show the square ABCD.

A) (2,1,4)
B) (1,3,3)
C) (2,1,3)
D) (2,3,1)
E) None of the above.

Question

The following is called the Chaos Game. Start with a square ABCD in which A is located at (0, 0), B is
located at (27, 0), C is located at (27, 27), and D is located at (0, 27). Then, roll a fair die. We will say
that A is the winner if we roll a 1, B is the winner if we roll a 2, C is the winner if we roll a 3, and D is
the winner if we roll a 4. If we roll a 5 or 6, we disregard the roll and roll again. Each roll of the die generates a point inside or on the boundary of the square according to the following rules.
 Start: Roll the die. Mark the winning vertex and call it P1.
 Step 1: Roll the die again. From P1 move two-thirds of the way straight towards the next
winning vertex. Mark this point and call it P2.
 Steps 2, 3, etc.: Continue rolling the die, each time moving to a point two-thirds of the way
from the last position to the winning vertex.
The grid below show the square ABCD.

A) (2,1,4) 
B) (1,3,3) 
C) (2,1,3) 
D) (2,3,1) 
E) None of the above.

Quizplus · Accepted Answer

The Answer of The following is called the Chaos Game. Start with a square ABCD in which A is located at (0, 0), B is
located at (27, 0), C is located at (27, 27), and D is located at (0, 27). Then, roll a fair die. We will say
that A is the winner if we roll a 1, B is the winner if we roll a 2, C is the winner if we roll a 3, and D is
the winner if we roll a 4. If we roll a 5 or 6, we disregard the roll and roll again. Each roll of the die generates a point inside or on the boundary of the square according to the following rules.
 Start: Roll the die. Mark the winning vertex and call it P1.
 Step 1: Roll the die again. From P1 move two-thirds of the way straight towards the next
winning vertex. Mark this point and call it P2.
 Steps 2, 3, etc.: Continue rolling the die, each time moving to a point two-thirds of the way
from the last position to the winning vertex.
The grid below show the square ABCD.

A) (2,1,4) 
B) (1,3,3) 
C) (2,1,3) 
D) (2,3,1) 
E) None of the above.

The Following Is Called the Chaos Game