TED-Ed: Dennis Shasha: Can you solve the stolen rubies riddle?

A merchant accused of corruption must play a game to determine the fine. He divides 30 rubies into three boxes, and an advisor must choose numbers to maximize ruby collection. The advisor uses strategic thinking and proof by contradiction to ensure a minimum win of 16 rubies, recovering more than half of the merchant's wealth.

What is the main reason the king decides to use a game to determine the merchant's fine?

• To ensure fairness in determining the fine

• To test the advisor's intelligence

• To punish the merchant more severely

• To entertain the crowd

What are the two constraints placed on the distribution of rubies in the boxes?

• Each box must have at least three rubies, and one box must have exactly five more rubies than another

• Each box must have at least one ruby, and one box must have double the rubies of another

• Each box must have at least two rubies, and one box must have exactly six more rubies than another

• Each box must have an equal number of rubies, and one box must have at least ten rubies

Why is it suggested to choose the same number for each box?

• To make the game more challenging

• To guarantee a minimum number of rubies won

• To ensure a fair distribution

• To confuse the merchant

What is the minimum number of rubies the advisor can guarantee to win?

• 10 rubies

• 12 rubies

• 16 rubies

• 20 rubies

What logical method is used to determine that at least two boxes have 8 or more rubies?

• Proof by induction

• Proof by contradiction

• Proof by exhaustion

• Proof by construction