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

Revision as of 22:50, 30 March 2011

Problem:

Define an ordered quadruple (a, b, c, d) as interesting if $1≤a<b<c<d≤10$ (Error compiling LaTeX. ! Package inputenc Error: Unicode character ≤ (U+2264)). (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) 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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