Difference between revisions of "2006 Cyprus MO/Lyceum/Problem 21"
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==Problem== | ==Problem== | ||
| − | + | A convex polygon has <math>n</math> sides and <math>740</math> diagonals. Then <math>n</math> equals | |
| + | |||
| + | A. <math>30</math> | ||
| + | |||
| + | B. <math>40</math> | ||
| + | |||
| + | C. <math>50</math> | ||
| + | |||
| + | D. <math>60</math> | ||
| + | |||
| + | E. None of these | ||
==Solution== | ==Solution== | ||
| − | {{ | + | The number of diagonals is <math>\frac{n(n-3)}{2} = 740 \Longrightarrow n(n-3) = 1480</math>. By either solving the [[quadratic equation]] or by substituting the answer choices, we get <math>n = 40 \Longrightarrow \mathrm{B}</math>. |
==See also== | ==See also== | ||
{{CYMO box|year=2006|l=Lyceum|num-b=21|num-a=22}} | {{CYMO box|year=2006|l=Lyceum|num-b=21|num-a=22}} | ||
| + | |||
| + | [[Category:Introductory Combinatorics Problems]] | ||
Revision as of 16:53, 15 October 2007
Problem
A convex polygon has 
sides and 
diagonals. Then equals
A. 
B. 
C. 
D. 
E. None of these
Solution
The number of diagonals is 
. By either solving the quadratic equation or by substituting the answer choices, we get 
.
See also
| 2006 Cyprus MO, Lyceum (Problems) | ||
| Preceded by Problem 21 |
Followed by Problem 22 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
