The Coin Weighing Puzzle is one of the most famous classic logic riddles in the world of problem-solving. It challenges both mathematical reasoning and strategic thinking. The task is simple yet tricky: out of 12 identical-looking coins, one is counterfeit; it’s either heavier or lighter than the others. You have only three chances to use a balance scale and determine which coin is odd and whether it’s heavier or lighter.
At first glance, this may seem impossible, but with the right logical approach, the puzzle can be solved perfectly. This riddle is often used in job interviews, logical reasoning exams, and IQ challenges because it tests how well a person can plan, eliminate possibilities, and use deduction under constraints.
Coin Weighing Puzzle Setup and Objective
You are given 12 coins that appear identical. However, one of them differs in weight; it may be either heavier or lighter. You are also given a two-pan balance scale that can tell which side is heavier, lighter, or balanced.
Objective:
Find the unique coin and determine whether it’s heavier or lighter using the balance no more than three times.
This puzzle requires precision, observation, and a systematic approach. The key lies in dividing and testing the coins smartly rather than randomly.
Step-by-Step Solution for The Coin Weighing Puzzle
To solve the Coin Weighing Puzzle, we’ll use logical division and elimination to ensure that every weighing provides maximum information.
Step 1: Divide the Coins into Three Groups
Start by dividing the 12 coins into three equal groups of 4 coins each:
- Group 1: Coins 1, 2, 3, 4
- Group 2: Coins 5, 6, 7, 8
- Group 3: Coins 9, 10, 11, 12
This setup ensures that your first weighing can test a balanced portion of the total coins, leaving the last group aside for comparison if needed.
Step 2: First Weighing
Weigh Group 1 (1, 2, 3, 4) against Group 2 (5, 6, 7, 8).
Scenario A: The scales balance
This means all 8 coins (Groups 1 and 2) are normal, and the odd coin is in Group 3 (9, 10, 11, 12).
Scenario B: The scales do not balance
This means the odd coin is in either Group 1 or Group 2. The direction of tilt also gives you a clue whether the fake coin is heavier or lighter.
At this point, you’ve eliminated one full group and halved your search space.
Step 3: Second Weighing (If the Scales Balanced in Step 2)
Now that you know the odd coin is in Group 3, pick three coins (9, 10, 11) from it and weigh them against three known normal coins (say, 1, 2, 3).
Scenario A1: The scales balance
If they balance, the odd coin is 12.
To check whether it’s heavier or lighter, compare coin 12 with any normal coin (for example, coin 1).
Scenario A2: The scales do not balance
If they don’t balance, then one of coins 9, 10, or 11 is the odd coin.
The direction of tilt shows whether the odd coin is heavier or lighter.
Now you’re ready for the final weighing.
Step 4: Second Weighing (If the Scales Did Not Balance in Step 2)
If the first weighing was unbalanced, you already know which group (1 or 2) contains the odd coin.
Suppose Group 1 was heavier; this means either a coin in Group 1 is heavier or a coin in Group 2 is lighter.
Now, take three coins from the heavier side and three coins from the lighter side and weigh them.
Scenario B1: The scales balance
If they balance, the odd coin is one of the remaining unweighed coins from those two groups. You can now identify it by comparing one of them with a normal coin.
Scenario B2: The scales do not balance
If they don’t balance, you’ve now narrowed down the odd coin to one of the coins being weighed.
By comparing any two of these coins, you can find which one is different and whether it’s heavier or lighter.
Step 5: Final Weighing
At this stage, you’ll have narrowed it down to two or three possible coins.
Use your third weighing to compare any two suspected coins or compare one with a known normal coin.
The outcome of this weighing will conclusively tell you:
- Which coin is the odd one.
- Whether it’s heavier or lighter.
Summary: The Coin Weighing Puzzle Steps
| Step | Action | What It Reveals |
|---|---|---|
| 1 | Divide 12 coins into 3 groups of 4 each | Creates 3 logical groups |
| 2 | Weigh Group 1 vs Group 2 | Identifies which group has the odd coin |
| 3 | If balanced, weigh 3 coins from Group 3 vs 3 normal coins | Narrows down to the odd coin |
| 4 | If unbalanced, rearrange coins and test again | Determines which group has the fake coin |
| 5 | Final weighing | Confirms the odd coin and whether it’s heavier or lighter |
Final Answer: Identifying the Odd Coin in Three Weighings
By following this step-by-step method, you can find the unique coin and determine whether it’s heavier or lighter, using only three weighings.
The key is not guesswork; it’s logic. By dividing, comparing, and eliminating, you turn an impossible-looking puzzle into a guaranteed win.
Why the Coin Weighing Puzzle is Popular?
The Coin Weighing Puzzle is a timeless classic because it combines mathematical reasoning, deductive logic, and strategic planning. It demonstrates how a limited number of tests can yield perfect information if used intelligently.
It’s widely used in:
- Job interviews at top companies like Google and Amazon.
- Math Olympiads and competitive exams.
- Logic puzzle books and educational training sessions.
This puzzle shows how structured reasoning can solve complex problems efficiently, without any guesswork.
Mathematical Insight Behind the Puzzle
Each weighing on the balance scale can have three possible outcomes:
- Left side heavier,
- Right side heavier,
- Both sides balance.
With three weighings, that gives 3³ = 27 possible outcomes.
Out of these, you can distinguish 24 possible states (12 coins × 2 possibilities, heavier or lighter).
That’s why 12 coins is the maximum number solvable in three weighings, it’s mathematically perfect!
Similar Logic Puzzles with Answers
Here are other puzzles that, like the Coin Weighing Puzzle, test logic, reasoning, and strategy:
1. The 100 Prisoners Hat Puzzle – Parity Logic
Setup: 100 prisoners guess hat colors with limited info.
Answer: Using parity, 99 survive, and sometimes all 100.
2. The River Crossing Puzzle – Wolf, Goat, and Cabbage
Setup: A farmer must cross a river with three items but can carry only one at a time.
Answer: Take the goat first, then the wolf, then the cabbage, and finally the goat again.
3. The Two Doors Riddle – Truth and Lies
Setup: Two guards, one lies, one tells the truth.
Answer: Ask one guard what the other would say, and choose the opposite door.
4. The Monty Hall Problem – Probability and Choice
Setup: Choose one of three doors; one hides a car, others goats.
Answer: Always switch, it doubles your winning chances.
5. The Blue Eyes Puzzle – Logic of Awareness
Setup: People don’t know their eye color until told at least one has blue eyes.
Answer: If n people have blue eyes, they leave on the nth night.