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 | + | 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 22:37, 28 April 2014
In a mathematical contest, three problems, 
, 
, and 
were posed. Among the participants there were 
students who solved at least one problem each. Of all the contestants who did not solve problem , the number who solved was twice the number who solved . The number of students who solved only problem was one more than the number of students who solved and at least one other problem. Of all students who solved just one problem, half did not solve problem . How many students solved only problem ?
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 | ||
