Why is the 12-coin problem harder?

You must also find whether the fake is heavier or lighter

Balance Scale Puzzles Quiz: Find the Fake Coin in Few Weighings

A two-pan scale gives three possible results each time, which is the secret behind many classic puzzles, and this balance scale puzzles quiz walks through them. Play an interactive set of 10 questions on splitting coins into thirds, nine coins in two weighings, the 12-coin problem, powers of three, the formula for unknown weights, Bachet's weight problem and information theory.

Start Balance Scale Puzzles Quiz

🎯 Daily Trivia Challenge • 🧠 10 Questions • ⏱️ 150 Seconds

Question 1 / 10 Time: 150s

Outcomes
How many outcomes can one weighing on a balance scale have?
Nine
How many weighings are needed to find one heavier coin among nine?
Split
What is the best first step with nine coins and one heavier?
Powers
With one heavier coin, how many coins can be checked in three weighings?
Twelve
How many weighings solve the classic 12-coin problem?
Unknown
Why is the 12-coin problem harder?
Eight
How many weighings find one heavier coin among eight?
Bachet
Which weights let you weigh any whole amount from 1 to 40 using both pans?
OnePan
If weights may only go in one pan, which set covers 1 to 15?
Theory
Which field explains why thirds are efficient?

Explanations: answer key for all 10 questions

Q1: How many outcomes can one weighing on a balance scale have?
Answer: Three
Left heavier, right heavier or equal.
Q2: How many weighings are needed to find one heavier coin among nine?
Answer: Two
Split them into three groups of three.
Q3: What is the best first step with nine coins and one heavier?
Answer: Weigh three against three
Thirds use all three outcomes.
Q4: With one heavier coin, how many coins can be checked in three weighings?
Answer: 27
That is 3 to the third power.
Q5: How many weighings solve the classic 12-coin problem?
Answer: Three
The fake may be heavier or lighter.
Q6: Why is the 12-coin problem harder?
Answer: You must also find whether the fake is heavier or lighter
Each result must narrow both questions.
Q7: How many weighings find one heavier coin among eight?
Answer: Two
Weigh three against three first.
Q8: Which weights let you weigh any whole amount from 1 to 40 using both pans?
Answer: 1, 3, 9 and 27
This is Bachet's weight problem.
Q9: If weights may only go in one pan, which set covers 1 to 15?
Answer: 1, 2, 4 and 8
This uses binary.
Q10: Which field explains why thirds are efficient?
Answer: Information theory
Each weighing gives at most three outcomes.

Balance Scale Puzzles Quiz – Find the Fake Coin in Few Weighings

Balance scale puzzles ask you to find a fake coin with as few weighings as possible. Each weighing has three outcomes, so dividing coins into three groups is usually best. With one heavier coin, two weighings can solve nine coins and three weighings can solve 27.

The classic 12-coin problem is harder: one coin is fake, but you do not know whether it is heavier or lighter. Three weighings are enough if each result is used to narrow both questions at once.

Related puzzles include Bachet's weight problem, where weights of 1, 3, 9 and 27 placed on either pan can weigh any whole amount up to 40. Information theory explains why using all three outcomes is so powerful.

What This Quiz Teaches

Puzzle fans will enjoy these questions.

How balance scales give information
How to split coins
Why the 12-coin problem is hard
Which weight sets work
Why powers of three matter

Did You Know?

The 12-coin puzzle became popular in the 1940s.
Drawing a decision tree helps solve it.
Interviewers sometimes ask these puzzles.
With 13 coins and unknown weight, three weighings are not always enough.
Digital scales make the puzzle much easier.