Difference between revisions of "1973 Canadian MO Problems/Problem 4"
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pair C=dir(120-(40)*(k+2)); | pair C=dir(120-(40)*(k+2)); | ||
D(A--B); | D(A--B); | ||
| − | |||
A=B;B=C; | A=B;B=C; | ||
} | } | ||
| − | |||
for(int k=0;k<3;++k) | for(int k=0;k<3;++k) | ||
{ | { | ||
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D(A1--B1); | D(A1--B1); | ||
D(A1--C1); | D(A1--C1); | ||
| + | } | ||
| + | for(int k=0;k<9;++k) | ||
| + | { | ||
| + | pair A=dir(120+(40)*(k)); | ||
| + | MP("P_{"+string(k)+"}",A,11,A); | ||
} | } | ||
</asy> | </asy> | ||
Latest revision as of 18:24, 8 October 2014
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); 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); } for(int k=0;k<9;++k) { pair A=dir(120+(40)*(k)); MP("P_{"+string(k)+"}",A,11,A); } [/asy]](http://latex.artofproblemsolving.com/8/3/4/8344776ea853dd08ddb05d7aea1fc48e2f92214a.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 |
