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Twenty Mock Mathcounts Sprint Round Practices
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Test 1 problem 26 solution
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Topic: Test 1 problem 26 solution (Read 4636 times)
yongcheng3315
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USAMO Winner
Posts: 2585
Test 1 problem 26 solution
«
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.
«
Last Edit: February 18, 2011, 07:04:57 PM by Andover 2011
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WWL2010
Math Coach
Mathcounts School Champion
Posts: 5
Re: Test 1 problem 26 solution
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Reply #1 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
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Problem Solving Skills for Mathcounts Competitions
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Test 1 problem 26 solution