Difference between revisions of "1966 IMO Problems/Problem 1"

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In a mathematical contest, three problems, <math>A</math>, <math>B</math>, and <math>C</math> were posed. Among the participants ther were <math>25</math> students who solved at least one problem each. Of all the contestants who did not solve problem <math>A</math>, the number who solved <math>B</math> was twice the number who solved <math>C</math>. The number of students who solved only problem <math>A</math> was one more than the number of students who solved <math>A</math> and at least one other problem. Of all students who solved just one problem, half did not solve problem <math>A</math>. How many students solved only problem <math>B</math>?
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In a mathematical contest, three problems, <math>A</math>, <math>B</math>, and <math>C</math> were posed. Among the participants there were <math>25</math> students who solved at least one problem each. Of all the contestants who did not solve problem <math>A</math>, the number who solved <math>B</math> was twice the number who solved <math>C</math>. The number of students who solved only problem <math>A</math> was one more than the number of students who solved <math>A</math> and at least one other problem. Of all students who solved just one problem, half did not solve problem <math>A</math>. How many students solved only problem <math>B</math>?
  
 
==Solution==
 
==Solution==

Revision as of 23:37, 28 April 2014

In a mathematical contest, three problems, $A$, $B$, and $C$ were posed. Among the participants there were $25$ students who solved at least one problem each. Of all the contestants who did not solve problem $A$, the number who solved $B$ was twice the number who solved $C$. The number of students who solved only problem $A$ was one more than the number of students who solved $A$ and at least one other problem. Of all students who solved just one problem, half did not solve problem $A$. How many students solved only problem $B$?

Solution

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See Also

1966 IMO (Problems) • Resources
Preceded by
First Question
1 2 3 4 5 6 Followed by
Problem 2
All IMO Problems and Solutions
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