Question 27
A quadruple $$(a, b, c, d)$$ of distinct integers is said to be balanced if $$a+c=b+d$$. Let $$S$$ be any set of quadruples $$(a, b, c, d)$$ where $$1\le a<b<d<c\le 20$$ and where the cardinality of $$S$$ is $$4411$$. Find the least number of balanced quadruples in $$S$$.
Correct Answer: 91
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