Can you solve the stolen rubies riddle? - Dennis Shasha

TL;DR

A corrupt merchant's wealth in Burmese rubies is up for grabs in a game of wits to determine restitution for his victims.

Transcript

One of the kingdom’s most prosperous merchants has been exposed for his corrupt dealings. Nearly all of his riches are invested in a collection of 30 exquisite Burmese rubies, and the crowd in the square is clamoring for their confiscation to reimburse his victims. But the scoundrel and his allies at court have made a convincing case that at least ... Read More

Key Insights

• 💁 The merchant's wealth is in the form of 30 Burmese rubies.
• 😃 The game of wits is proposed because determining which portion of the rubies were obtained illegitimately is difficult.
• 🗂️ The rules of the game involve the merchant discreetly dividing the rubies among three boxes and you selecting numbers on cards.
• #️⃣ Picking the same number for each card allows you to maximize the minimum number of rubies you will receive.
• 😉 By analyzing the worst-case scenario, you can determine the minimum number of rubies you are guaranteed to win.
• 📞 To guarantee receiving more than half of the merchant's rubies, you need to select a number that ensures you will receive at least 16 rubies.

Questions & Answers

Q: What is the objective of the game of wits?

The objective is to guarantee the largest possible fine for the merchant and compensate his victims by selecting the most advantageous numbers.

Q: How can you ensure you receive more than half of the merchant's rubies?

To ensure this, you need to pick a number that guarantees you will receive at least 16 rubies, which is calculated using a proof by contradiction.

Q: What constraints are placed on the merchant's distribution of rubies?

The merchant must distribute at least two rubies in each box, and one box must have exactly six more rubies than another.

Q: How do you determine the minimum number of rubies you are guaranteed to win?

By assuming the worst-case scenario, where the merchant arranges the rubies to minimize your winnings, you can calculate the minimum number of rubies you are guaranteed to win.

Summary & Key Takeaways

• A prosperous merchant with corrupt dealings is facing confiscation of his 30 Burmese rubies to reimburse his victims.

• A game of wits is proposed between the merchant and the king's advisor (you) to determine the fine.

• The merchant can discreetly divide the rubies into three boxes, and you must write numbers on cards to determine the number of rubies you will receive from each box.