Key insights

• ⚖️ Divide 12 identical coins into three piles of four for weighing
• 🎚️ Use balance scale to narrow down possible locations of the fake coin
• 🔢 Mark authentic coins with zero to keep track of results
• ➕➖ Mark the coins in each pile with plus or minus based on their weight
• 🔄 Strategically replace coins on the scale to remove ambiguity
• ⚖️ Weigh the previously heavier side against a regular coin to identify the lighter coin
• 🔍 Weigh two of the three minus coins against each other to find the lighter one
• 🔄 Repeat the process for the three plus coins to find the heavier one

Q&A

• How does the protagonist use the weighing method to expose the counterfeiting lord?

  The protagonist weighs the previously heavier side against a regular coin to identify the lighter coin. They weigh two of the three minus coins against each other to find the lighter one. If the two sides balance, the third coin is counterfeit; if not, the lighter one is. They repeat the process for the three plus coins to find the heavier one. The protagonist's method impresses the Emperor and exposes the counterfeiting lord.

• What strategic steps are taken to identify the fake coin in two more steps?

  The remaining four coins are marked with zeros as the fake one is on the scale. Strategically replacing the coins on the scale to remove ambiguity by replacing three plus coins with three minus coins and then with three zero coins. Analyzing the result to identify the remaining plus coin as the heavier one.

• How is the plus/minus markings method used to identify the fake coin among the 12?

  The method entails using a balance scale to divide the coins into three piles of four. If two piles balance, the fake coin is in the third pile. Marking the coins in each pile with plus or minus based on their weight, and using the marked coins to identify the fake coin if the two piles don't balance.

• What method is used to find the fake coin among the 12 using a balance scale and markers?

  The method involves dividing the 12 coins into three piles of four, using a balance scale to narrow down possible locations of the fake coin, and marking authentic coins with zero to keep track of results. Then, weighing three marked coins against three unmarked coins to find the fake.

• How many attempts does the mathematician have to identify the counterfeit coin?

  The mathematician has three attempts to identify a counterfeit coin using a scale and the given coins. The Emperor allows only three attempts with the scale before being thrown back into the dungeon.

• What is the challenge presented to the mathematician?

  The mathematician is imprisoned but has a chance to earn freedom by identifying a counterfeit coin among 12 identical coins using a balance scale.

• 00:07 The mathematician is imprisoned but given a chance to earn freedom by identifying a counterfeit coin among 12 identical coins using a balance scale.
• 00:45 You have three attempts to identify a counterfeit coin using a scale and the given coins.
• 01:25 A method to find a fake coin among 12 using a balance scale and markers. Divide coins into piles, use balance scale to narrow down possibilities, and mark authentic coins with zero to keep track.
• 02:06 A method for finding a fake coin among 12 using a balance scale and plus/minus markings.
• 02:42 Strategically replace coins on the scale to identify the fake one in two more steps.
• 03:27 The protagonist uses a weighing method to identify counterfeit coins and successfully exposes the counterfeiting lord.