Outsmarting a Corrupt Merchant: The Stolen Rubies Riddle

Imagine a kingdom where a wealthy merchant is caught in corrupt dealings. The townspeople demand justice – specifically, the confiscation of his 30 exquisite Burmese rubies to compensate his victims. The king, in a Solomon-like move, decides the fine will be determined by a game of wits between the merchant and you, the king's clever advisor.

Can you devise a strategy to outsmart the merchant and recover the greatest number of rubies for the wronged citizens?

The Ruby Game: Rules of Engagement

The rules are laid out clearly:

• The merchant discreetly divides the 30 rubies among three boxes.
• You receive three cards and must write a number between 1 and 30 on each card.
• You place one card in front of each box.
• The boxes are opened.
• If a box contains at least as many rubies as the number on your card, you receive the number of rubies indicated on the card.
• However, if your number exceeds the actual number of rubies in the box, the merchant keeps the entire box.

The king adds two crucial constraints:

• Each box must contain at least two rubies.
• One of the boxes must contain exactly six more rubies than another box.

With the stage set, the merchant hides the gems. The question is: Which numbers should you choose to guarantee the largest possible fine for the merchant and the greatest compensation for his victims?

Decoding the Optimal Strategy

The key to solving this riddle lies in identifying the worst-case scenario. You must assume the merchant is trying to minimize your winnings, knowing your chosen numbers.

Since you don't know which boxes contain more or fewer rubies, the optimal strategy is to write the same number on all three cards. But what number guarantees the best outcome?

Let's consider an example: Suppose you write "9" on each card. The merchant could allocate the rubies as 8, 14, and 8. In this case, you'd only receive 9 rubies from the middle box.

However, you can be certain that at least two boxes contain a minimum of 8 rubies. Here's the logic:

• Assume the opposite: that two boxes have 7 or fewer rubies.
• These cannot be the two boxes that differ by 6 rubies (as each box must have at least 2).
• Therefore, the third box would have at most 13 rubies (7 + 6).
• The total rubies in all three boxes would then be at most 27 (7 + 7 + 13), which is less than the total of 30. This contradicts the initial condition.

Therefore, at least two boxes must contain 8 or more rubies.

The Winning Move

If you write "8" on all three cards, you're guaranteed to receive at least 16 rubies. This is the best you can guarantee. Consider the 8, 14, 8 scenario again – it demonstrates the limitation.

By choosing "8" for each box, you recover more than half of the merchant's ill-gotten fortune, providing significant restitution to the public.

The Power of Logic

This riddle highlights the power of logical deduction and strategic thinking. By considering the worst-case scenario and using proof by contradiction, you can devise a strategy that guarantees a favorable outcome, even when faced with uncertainty.

While the merchant may retain some of his rubies, his reputation is tarnished, and justice is partially served, thanks to your cleverness.