Given: 5 clues, each with a hint code and digit and position correctness information. Crack the 3 digit number lock puzzle with 194 in minimum steps.
The Number Lock Puzzle with 194
Clue 1. Code 1 9 4: One digit is correct but in the wrong place.
Clue 2. Code 6 3 0: One digit is correct but in the wrong place.
Clue 3. Code 0 2 4: Two digits are correct — 1 in the right place and 1 in the wrong place.
Clue 4. Code 4 9 1: One digit is correct and in the right place.
Clue 5. Code 6 4 2: Two digits are correct but both are in the wrong places.
Solve the puzzle in minimum steps.
Time to solve: 15 minutes.
Hints: Spot a rare digit pattern in the clues. Analyze multiple clues with the pattern together. Use the common digit patterns in multiple clues to identify incorrect and correct digits.
Solution to the 3 Digit Number Lock Puzzle with 194 in Minimum Steps
A scan through the 5 clues revealed a rare digit pattern - the single digit 4 is common in 4 clues. Following a golden rule of combined clue analysis, all four clues are analyzed together in the first step.
Step 1: Identify the first correct digit by false assumption based reasoning and follow up to reveal the other correct digits
Choose Clues 1, 3, 4, and 5 for analysis, as they all share the digit 4.
Golden rule: Analyze all clues having one or more than one digits common together to maximize breakthroughs.
Clue 1. Code 1 9 4: One digit is correct but in the wrong place.
Clue 3. Code 0 2 4: Two digits are correct — 1 in the right place and 1 in the wrong place.
Clue 4. Code 4 9 1: One digit is correct and in the right place.
Clue 5. Code 6 4 2: Two digits are correct but both are in the wrong places.
- False assumption based reasoning: Assume common digit 4 is incorrect. Then:
- In Clue 1, the correct digit must either be 1 or 9, in Clue 3, the two correct digits must be 0 and 2, and in Clue 5, the two correct digits must be 6 and 2 - in short, number of correct digits would be 4. But, this is impossible in a 3 digit number lock.
- Conclusions:
- 4 must be correct and in leftmost position by Clue 4.
- In Clue 3, it is the correct digit but in wrong place.
- Partial code [ 4 ? ? ].
- Positional conflict: In Clue 3, digit 4 being wrongly placed as its code position is leftmost, the second probable correct digit 0 is in correct leftmost place in the clue.
- 0 is wrong suffering from positional conflict with 4 in the correct code.
- Conclusion: By elimination, 2 is the second correct digit in correct place in Clue 3. Partial code: [ 4 2 ? ].
- Additional information - maximum information extraction in an analytical step: In Clue 5, digits 2 and 4 being correct, digit 6 is incorrect. In Clue 3, digit 0 is already identified incorrect. In Clue 4, digit 4 is the only correct digit in its place, and digits 1 and 9 incorrect none of which can occupy the single vacant rightmost place in the correct code. A new clue with a new digit needs to be analyzed.
Step 2: Identify the third correct digit looking for a new digit in a promising clue
With all four clues having been exhausted in possibilities of any additional breakthrough, the last Clue 2 must be taken up to crack the code.
Clue 2. Code 6 3 0: One digit is correct but in the wrong place.
- Digits 6 and 0 are wrong as deduced in additional information.
- Remaining digit 3 must be the third correct digit in the rightmost position.
Solution: Lock opening code: [ 4 2 3 ].
A two step solution using all five clues.
Lessons Learned from the Solution
- Use all clues with a digit common for breakthrough: Analyzing clues with digit 4 (Clues 1,3,4,5) helped identify the as correct.
- False assumption based reasoning: Assuming 4 incorrect led to contradiction (too many digits required), proving it correct and its correct place as leftmost.
- Positional conflict resolves second correct digit: Clue 3 produced second correct digit 2 by elimination of 0 suffering from positional conflict with digit 4 in leftmost position.
- Extraction of maximum information in an analytical step: Along with incorrect digit 0 in Clue 3, digit 6 is also identified as incorrect in Clue 5.
- Look for new avenues when all others are exhausted: Clue 2 provided the third correct digit 3, as digits 0 and 6 are already identified as incorrect.
- Use minimum number of steps to draw maximum conclusions: Except all the conclusions drawn in Step 1, discovery of the last digit 3 needed an additional step 2 using information gleaned in the earlier step.
This solution efficiently uses clues in a reasoning chain, minimizing steps and avoiding random trials.
To enjoy solving many more such number lock puzzles, click here.
Puzzles you may enjoy
Easy to hard brain teasers with systematic solutions
Challenging brain teasers with solutions: Long list.
This will always be the most up-to-date full list with the brain teasers classified into categories that can be browsed separately.