Problem Solving Skills for Mathcounts Competitions

Book Store => Bookstore => Twenty Mock Mathcounts Sprint Round Practices => Topic started by: yongcheng3315 on February 18, 2011, 07:04:15 PM

Title: Test 1 problem 26 solution
Post by: yongcheng3315 on February 18, 2011, 07:04:15 PM

problem 26. The sum of n interior angles and one exterior angle of a convex n-gon is 1350 degrees. Find n.

Solution:

Let n be the number of sides on the convex n-gon, and m be the exterior angle.

We know that

(n-2)*180+m = 1350

It becomes:

180n+m = 1710

This is a Diophantine equation. (Students need to be very familar for this kind of equations).
We use the following way to sovle it:

m = 1710   mod 180

We also know that m < 180.

So m = 90

n =9.

Title: Re: Test 1 problem 26 solution
Post by: WWL2010 on February 22, 2011, 05:03:54 PM

 Would you give the solutions:

--test 2, #7, #20, 23 and 29
--test 3, #22, 28, 29 and 30
--test 4,#8, #14, #25, #30