Difference between revisions of "2002 IMO Problems/Problem 1"
(Created page with "<math>S</math> is the set of all <math>(h,k)</math> with <math>h,k</math> non-negative integers such that <math>h + k < n</math>. Each element of <math>S</math> is colored red...") |
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− | <math>S</math> is the set of all <math>(h,k)</math> with <math>h,k</math> non-negative integers such that <math>h + k < n</math>. Each element of <math>S</math> is colored red or blue, so that if <math>(h,k)</math> is red and <math> | + | <math>S</math> is the set of all <math>(h,k)</math> with <math>h,k</math> non-negative integers such that <math>h + k < n</math>. Each element of <math>S</math> is colored red or blue, so that if <math>(h,k)</math> is red and <math>h' \le h,k' \le k</math>, then <math>(h',k')</math> is also red. A type <math>1</math> subset of <math>S</math> has <math>n</math> blue elements with different first member and a type <math>2</math> subset of <math>S</math> has <math>n</math> blue elements with different second member. Show that there are the same number of type <math>1</math> and type <math>2</math> subsets. |
Revision as of 00:25, 19 November 2023
is the set of all
with
non-negative integers such that
. Each element of
is colored red or blue, so that if
is red and
, then
is also red. A type
subset of
has
blue elements with different first member and a type
subset of
has
blue elements with different second member. Show that there are the same number of type
and type
subsets.