In this number lock puzzle with clue code 682 and 5 clues, each clue describes position and correctness of 3 digits in its code. Can you crack the code?
The Number Lock Puzzle with Clue Code 682
Following shows five clues each with a 3 digit code for a number lock. Each clue describes the correctness of the digits and their positions in the lock opening code. Find the code to open the lock.
Clue 1: Code 682: One digit is right and is in its place.
Clue 2: Code 645: One digit is right and is in the wrong place.
Clue 3: Code 206: Two digits are right, but both are in the wrong place.
Clue 4: Code 738: All digits are wrong.
Clue 5: Code 780: One digit right and is in the wrong place.
From these five clues, find the 3 digit code that will open the number lock.
Your challenge: try to find the most efficient solution using least number of clues.
Time to solve: 10 minutes.
Solution to the 3 digit number lock puzzle with clue code 682
What would be the very first step that you should take to solve the puzzle easily? Can it be,
- An attempt to find the correct place of a digit in the lock opening code? But then, the question you face: correct place of which digit, the digit that must be one of the three correct digits?
See, you don't really have any option other than,
- To find a correct digit in your first important step!
Then again, if it is not possible to find a correct digit in your first step, but you find, you can easily identify an incorrect digit?
Yes, this realization modifies your objective of taking the first important step by including incorrect digit identification as well.
Why?
Because when you know a digit as incorrect, a new clue can lead you to easily know one or more than one correct digits.
Step 1. Identify correct or incorrect digits
If you find no single clue can help you identify a correct or an incorrect digit? That is when, you would look for more than one clue and analyze the clues together to discover a hidden pattern. The pattern that tells you, yes, this digit must be incorrect (or correct.
What usually happens - no clue alone can identify a correct or incorrect digit, and the commonly occurring hidden pattern in the clues is:
- More than one suitable clue with same digit appearing, but with conflicting position and correctness descriptions will serve your purpose (position and correctness conflict).
Such clues are Clue 1 and Clue 6.
Clue 1: Code 682: One digit is right and is in its place.
Clue 2: Code 645: One digit is right and is in the wrong place.
- Digit 6 cannot occupy the same position in both and have correct place in one clue and wrong place in the other.
- Digit 6 is the first wrong digit identified.
Which clue should you analyze next? Common sense logic tells you to take up next Clue 3, as it includes the wrong digit 6 (link reference technique).
Clue 3: Code 206: Two digits are right, but both are in the wrong place.
- With digit 6 wrong, first two correct digits identified are 0 and 2 - your objective satisfied.
What should you do next? Again, apply your common sense reasoning.
- As you know two digits as correct, it is the right time to identify their correct places in the lock opening code, isn't it?
Step 2. Find the correct digit placements
Take up Clue 1 again as its code includes correct digit 2 (link reference again).
Clue 1: Code 682: One digit is right and is in its place.
- Digit 2 is to be placed in the rightmost position.
Turn to Clue 3 again in which two correct digits 0 and 2 both are wrongly placed.
Clue 3: Code 206: Two digits are right, but both are in the wrong place.
Rightmost position already taken up by correct digit 2, digit 6 is incorrect, and middle position for digit 0 is wrong.
- Position of the second correct digit 0 must be leftmost.
- Correct code is of the form 0 ? 2.
Step 3. Find the third right digit and solve the 3 digit number lock riddle with 5 clues
Analyze Clue 2 with one of the two digits 4 or 5 correct as digit 6 is wrong.
Clue 2: Code 645: One digit is right and is in the wrong place.
The correct digit is in the wrong place.
- Digit 4 occupying the only available supposedly correct position cannot be the right digit (positional constraint).
- The third right digit is 5 in middle position.
The code to open the lock is 0 5 2.
Clues 4 and 5 not needed. You have discovered your most efficient solution.
Waste nothing. Following the powerful inventive principle of free resource use, check the unused Clues 4 and 5 for verifying the correctness of the lock opening code "0 5 2".
Clue 4: Code 738: All digits are wrong.
- None of the digits 7, 3 or 8 is in our code "0 5 2". Code verified.
Clue 5: Code 780: One digit right and is in the wrong place.
- Only the digit 0 is in your lock opening code "0 5 2", and its leftmost position tallies with the position description. Code verified.
End note
The key to quick solutions of reasoning puzzles is processing the most suitable clue or condition either individually or together with other clues.
Strategies, techniques and problem solving principles used
- Position and correctness conflict: In two clues, a digit is common with conflicting position and correctness descriptions. By analyzing Clues 1 and 2, digit 6 is identified as a wrong one.
- Link reference technique: Analyzing a clue referring to an already identified correct or incorrect digit reveals other correct or incorrect digits. Clue 3, which includes wrong digit 6 reveals two correct digits 0 and 2 at one go.
- Positional constraint: In a clue, a digit in the only available free position in the partially formed lock opening code reveals the third correct digit. In Clue 2 with code 645, digit 4 occupied the only free middle position in the partially formed lock opening code "0 ? 2", but the clue description stated, "One digit is right and is in the wrong place." This identified digit 5 as the third correct digit in the middle position.
- Your most efficient solution: The solution used only 3 out of 5 given clues and should be your most efficient solution.
- Inventive principle of free resource use: The resources of the unused Clues 4 and 5 were free and so you have used the two for verifying the correctness of the solution.
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