The Four Rings Story

Number Theory Level 4

Four teen boys, wanted to impress their girlfriends on Valentine's day. They decided to pool their resources and buy four identical gold rings.

Aaron and Calvin each contributed the same amount of gold, while Bart contributed the same amount of gold as Dexter.

They went to a goldsmith's and the apprentice weighed all the four contributions, and concluded that all the four could have 4 rings each, with more rings to spare and no spare gold. However, the sharp eyed master who was at hand, scolded the apprentice for multiplying the weights, instead of adding them.

He then apologized to the four people and said that exactly two rings could be made with the available gold.

If each the four friends contributed an integer amount in grams of gold, what is the minimum weight that a ring could have in grams?


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