Difference between revisions of "1983 USAMO"

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==1983 USAMO Problems==
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'''1983 [[USAMO]]''' problems and solutions.  The first link contains the full set of test problems.  The rest contain each individual problem and its solution.
  
==Problem 1==
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* [[1983 USAMO Problems|Entire Test]]
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** [[1983 USAMO Problems/Problem 1|Problem 1]]
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** [[1983 USAMO Problems/Problem 2|Problem 2]]
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** [[1983 USAMO Problems/Problem 3|Problem 3]]
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** [[1983 USAMO Problems/Problem 4|Problem 4]]
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** [[1983 USAMO Problems/Problem 5|Problem 5]]
  
If six points are chosen sequentially at random on the circumference of a circle, what is the probability that the triangle formed by the first three is disjoint from that formed by the second three?
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== See Also ==
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* [[Mathematics competitions]]
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* [[Mathematics competition resources]]
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* [[Math books]]
  
==Problem 2==
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{{USAMO box|year=1983|before=[[1982 USAMO]]|after=[[1984 USAMO]]}}
Prove that the zeros of
 
 
 
<cmath>x^5+ax^4+bx^3+cx^2+dx+e=0</cmath>
 
 
 
cannot all be real if <math>2a^2<5b</math>.
 
 
 
[[Solution]]
 

Latest revision as of 12:42, 18 July 2016

1983 USAMO problems and solutions. The first link contains the full set of test problems. The rest contain each individual problem and its solution.

See Also

1983 USAMO (ProblemsResources)
Preceded by
1982 USAMO
Followed by
1984 USAMO
1 2 3 4 5
All USAMO Problems and Solutions