Identifying the Counterfeit Coin

The video presents a problem where a mathematician must identify a counterfeit coin among 12 using a balance scale only three times. The solution involves strategic weighing and marking of coins to determine the fake one, which is either slightly heavier or lighter. The process is broken down into initial, second, and final weighings, with each step narrowing down the possibilities until the counterfeit is identified. The mathematician's success leads to freedom, while the counterfeiter is punished.

What is the main challenge the mathematician faces in the problem?

• Counting the total number of coins

• Identifying the heaviest coin

• Finding the counterfeit coin with limited weighings

• Balancing all coins equally

How are the coins initially divided for the first weighing?

• Into four groups of three

• Into three groups of four

• Into six groups of two

• Into two groups of six

What does it mean if the first two piles on the scale balance?

• The counterfeit is among the eight coins on the scale

• The counterfeit is among the four coins not on the scale

• All coins are real

• The counterfeit is heavier

What is the purpose of marking coins with a zero, plus, or minus?

• To mark the coins that are real

• To indicate their weight relative to others

• To track which coins have been weighed

• To identify the heaviest coin

If two marked coins are weighed and balance, what can be concluded?

• The third unweighed coin is counterfeit

• All are real

• One of them is counterfeit

• Both are counterfeit

What is the next step if the first weighing does not balance?

• Mark the heavier side with a minus

• Mark the lighter side with a plus

• Mark the heavier side with a plus and the lighter with a minus

• Mark all coins with zeros

What is the strategy if the previously heavier side remains heavier after reassembly?

• The remaining plus coin is heavier

• The remaining minus coin is lighter

• Either the plus or minus coin is counterfeit

• The remaining zero coin is counterfeit

What should be done if the previously heavier side becomes lighter?

• Weigh two of the zero coins against each other

• Weigh the remaining coins against a regular coin

• Weigh two of the minus coins against each other

• Weigh two of the plus coins against each other

What indicates that one of the three plus coins removed is the counterfeit?

• The scale balances after substitution

• The scale tips to the heavier side

• The scale tips to the lighter side

• The scale does not move

What is the final outcome for the mathematician?

• He remains in the dungeon

• He fails to identify the counterfeit

• He identifies the counterfeit and is freed

• He is given more time to solve the problem