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>? | 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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{{IMO box|year=1966|before=First Question|num-a=2}} | {{IMO box|year=1966|before=First Question|num-a=2}} | ||
Revision as of 03:40, 14 October 2013
In a mathematical contest, three problems, 
, 
, and 
were posed. Among the participants ther 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 ?
See Also
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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 | ||
