Difference between revisions of "2014 AMC 12B Problems/Problem 12"
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<math>(1, 1, 1)</math> | <math>(1, 1, 1)</math> | ||
− | It should be clear that <math>|S|</math> is simply <math>|T| - t</math>, where <math> | + | It should be clear that <math>|S|</math> is simply <math>|T| - t</math>, where <math>t</math> is the number of triples <math>(d, e, f)</math> such that there exists at least one triple <math>(kd, ke, kf)</math> where <math>k \ge 1</math> and <math>k \in \mathbb{N}</math>. So, <math>t</math> is... and the answer is ... ... |
Revision as of 22:16, 20 February 2014
Solution
Define to be the set of all triples
such that
,
, and
. Now we enumerate the elements of
:
It should be clear that is simply
, where
is the number of triples
such that there exists at least one triple
where
and
. So,
is... and the answer is ... ...