Difference between revisions of "1988 IMO Problems/Problem 2"
Durianaops (talk | contribs) (→Problem) |
Durianaops (talk | contribs) (→Problem) |
||
| Line 12: | Line 12: | ||
For which values of <math>n</math> can one assign to every element of <math>B</math> one of the numbers <math>0</math> and <math>1</math> in such a way that <math>A_i</math> has <math>0</math> assigned to exactly <math>n</math> of its elements? | For which values of <math>n</math> can one assign to every element of <math>B</math> one of the numbers <math>0</math> and <math>1</math> in such a way that <math>A_i</math> has <math>0</math> assigned to exactly <math>n</math> of its elements? | ||
| + | |||
| + | == Solution == | ||
| + | |||
| + | {{Alternate solutions}} | ||
== See Also == | == See Also == | ||
{{IMO box|year=1988|num-b=1|num-a=3}} | {{IMO box|year=1988|num-b=1|num-a=3}} | ||
Revision as of 07:23, 28 March 2019
Problem
Let 
be a positive integer and let 
be subsets of a set 
.
Suppose that
(a) Each 
has exactly 
elements,
(b) Each 
contains exactly one element, and
(c) Every element of belongs to at least two of the .
For which values of can one assign to every element of one of the numbers 
and 
in such a way that has assigned to exactly of its elements?
Solution
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
See Also
| 1988 IMO (Problems) • Resources | ||
| Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
| All IMO Problems and Solutions | ||
