Difference between revisions of "1983 USAMO"
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==1983 USAMO Problems== | ==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. | ||
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| + | [[1983 USAMO Problem 1]] | ||
==Problem 1== | ==Problem 1== | ||
Revision as of 18:18, 13 November 2011
1983 USAMO Problems
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
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?
Problem 2
Prove that the zeros of
![\[x^5+ax^4+bx^3+cx^2+dx+e=0\]](http://latex.artofproblemsolving.com/9/0/4/9049ba78fdefb11bd3a89101dac429cad1017dce.png)
cannot all be real if 
.
