Difference between revisions of "2011 AIME II Problems/Problem 6"

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Problem:
 
Problem:
  
Define an ordered quadruple (a, b, c, d) as interesting if <math>1 \le a<b<c<d≤10</math>. (Okay, if you go to edit page you can see that those wierd a's are supposed to be "less than or equal to" signs, somebody please fix this)
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Define an ordered quadruple (a, b, c, d) as interesting if <math>1 \le a<b<c<d \le 10</math>, and a+d>b+c. How many ordered quadruples are there?
and a+d>b+c. How many ordered quadruples are there?
 
  
 
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Revision as of 09:01, 31 March 2011

Problem:

Define an ordered quadruple (a, b, c, d) as interesting if $1 \le a<b<c<d \le 10$, and a+d>b+c. How many ordered quadruples are there?


Solution:

There is probably some really complicated formula for this, but as I didnt know it and had 3 hours to "do my best", I listed all possible combinations out. The answer is 80.

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