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IOQM 2023-24 P-27

Source:

September 3, 2023

Problem Statement

A quadruple (a,b,c,d)(a,b,c,d) of distinct integers is said to be balancedbalanced if a+c=b+da+c=b+d. Let S\mathcal{S} be any set of quadruples (a,b,c,d)(a,b,c,d) where 1⩽a<b<d<c⩽201 \leqslant a<b<d<c \leqslant 20 and where the cardinality of S\mathcal{S} is 44114411. Find the least number of balanced quadruples in S.\mathcal{S}.
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