2011 AIME II Problems/Problem 6

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Problem:

Define an ordered quadruple (a, b, c, d) as interesting if $1 \le a<b<c<d≤10$ (Error compiling LaTeX. ! Package inputenc Error: Unicode char \u8:≤ not set up for use with LaTeX.). (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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