1973 Canadian MO Problems/Problem 4
Problem
![[asy] size(200); pair A=dir(120), B=dir(80); for(int k=0;k<9;++k) { pair C=dir(120-(40)*(k+2)); D(A--B); MP("P_{"+string(k)+"}",A,11,A); A=B;B=C; } for(int k=0;k<3;++k) { pair A1=dir(120-(40)*(3*k)); pair B1=dir(120-(40)*(3*k+2)); pair C1=dir(120-(40)*(3*k+3)); D(A1--B1); D(A1--C1); } [/asy]](http://latex.artofproblemsolving.com/9/9/5/995f3dc66d6eb461860a3cefdfe833ed696095eb.png)
The figure shows a (convex) polygon with nine vertices. The six diagonals which have been drawn dissect the polygon into the seven triangles: 
. In how many ways can these triangles be labeled with the names 
so that 
is a vertex of triangle 
for 
? Justify your answer.
Solution
See also
| 1973 Canadian MO (Problems) | ||
| Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 | Followed by Problem 5 |
