Crack the five clue number lock puzzle with code 241 in a clue. The clues are with a 3 digit code and correctness descriptions of digits and positions.
The 3 Digit Number Lock Puzzle with Code 241 in a Clue
Following shows five clues each with a 3 digit hint code for a number lock and descriptions of the correctness of digits and positions. Find the code to open the lock.
Clue 1: Code 2 4 1 : One digit right and in right position.
Clue 2: Code 4 1 3 : All digits are wrongly placed.
Clue 3: Code 5 3 2 : Two digits right but wrongly placed.
Clue 4: Code 3 4 7 : One digit right but wrongly placed.
Clue 5: Code 7 5 1 : Two digits right but wrongly placed.
Find the 3 digit code that will open the number lock.
Time to crack the code: 10 minutes.
Solution to the 3 Digit Number Lock Puzzle with Code 241 in a Clue
Your first step? It must be to find a correct or incorrect digit as,
- Trying to find the correct place before knowing the correct digit defies commonsense.
Why the incorrect digit? Because,
- Knowing a digit to be incorrect should surely lead you to find other correct digits from a new clue.
Step 1. Find a correct or an incorrect digit
A brief scan through the clues tells you, it isn't possible to find a correct or incorrect digit from a single clue. Searching for a pair of suitable clues for the breakthrough, you identify a special pattern in clues 1 and 5.
- One digit is common in both the clues, appear in the same position in the clue codes and have different correctness descriptions of position.
Clue 1: Code 2 4 1 : One digit right and in right position.
Clue 5: Code 7 5 1 : Two digits right but wrongly placed.
- If by Clue 1, digit 1 the right digit, rightmost position must be its correct position, but Clue 5 violates this placement.
- Conclusion: Digit 1 is incorrect.
This is an important breakthrough pattern of Position and correctness conflict in solving number lock puzzles.
By the same pattern, from Clue 1 and Clue 4, digit 4 is wrong.
Clue 1: Code 2 4 1 : One digit right and in right position.
Clue 4: Code 3 4 7 : One digit right but wrongly placed.
- Digit 4 occupies middle position in both the clues. If it is the right digit by Clue 1, its position is also correct, but by Clue 4 its position cannot be in the middle.
- Conclusion: Digit 4 is incorrect. Also, we know digit 1 incorrect.
Step 2. Identify the correct position of the right digit
From Clue 1, leftmost position goes to digit 2.
Clue 1: Code 2 4 1 : One digit right and in right position.
- Both 1 and 4 are incorrect.
- Conclusion: Right digit 2 takes leftmost place in the lock opening code.
Step 3: Find the other two correct digits and their positions
Clue 5 gives the breakthrough as it includes the incorrect digit 1 (link reference technique).
Clue 5: Code 7 5 1 : Two digits right but wrongly placed.
- Conclusion: With digit 1 wrong, digits 5 and 7 are the other two correct digits with positions either middle or rightmost.
From Clue 4 find the solution (it includes the correct digit 7 - link reference again).
Clue 4: Code 3 4 7 : One digit right but wrongly placed.
- Conclusion: The single right digit 7 occupies a wrong 3rd position.
- Conclusion: Digit 7 must be in the middle position (as leftmost position is occupied by digit 2).
- Conclusion: Digit 5 must be the rightmost.
Correct code to open the number lock is 2 7 5.
Clues 2 and 3 not needed.
Use these free resources of two unused clues to verify the correctness of the solution.
Clue 2: Code 4 1 3 : All digits are wrongly placed.
- None of the three digits are right. Code 275 verified.
Clue 3: Code 5 3 2 : Two digits right but wrongly placed.
- Both the correct digits, 2 and 5 are wrongly placed. Code 275 is verified again.
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.
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