Question: Sam has put sweets in five jars in such a way that no jar is empty and no two jars contain the same number of sweets. Also, any three jars contain more sweets in total than the total of the remaining two jars.
What is the smallest possible number of sweets altogether in the five jars?
Let the number of sweets in jars 1, 2, 3, 4 & 5 be a, b, c, d & e respectively.
We have a>0, b>0, c>0, d>0 & e>0
We also have a ≠ b ≠ c ≠ d ≠ e
What do I do next to solve this question. Is my approach good?