Given 5 clues, each with a 3 digit code and hints on correct digits and placements. Real challenge: Open the 3 digit number lock 342 using first four clues.
Real Puzzle Challenge: Open the 3 Digit Number Lock 342 Using First 4 Clues
Find the 3 digit code from first four of the five clues to open the number lock:
Clue 1: Code 3 4 2 : One digit right but wrongly placed.
Clue 2: Code 2 7 3 : One digit right but wrongly placed.
Clue 3: Code 1 6 5 : Two digits right and are well placed.
Clue 4: Code 8 5 3 : Two digits right but in wrong places.
Clue 5: Code 2 6 4 : Nothing is correct.
Time to solve this real challenge: 20 minutes.
But you may first like to meet the easier challenge of finding the number lock code using ANY four clues.
Time to solve: 5 minutes.
Solution to the Easier Puzzle Challenge: Open the 3 Digit Number Lock 342 Using ANY Four Clues
Objective, identify maximum number of incorrect digits in one step and use this set of incorrect digits as valuable resources to identify correct digits.
Step 1: Identify as many incorrect digits as possible and identify correct digits using this information
Clue 5 is the natural first favorite as it helps to identify three digits as wrong at one stroke.
Clue 5: Code 2 6 4 : Nothing is correct.
- Digits 2, 4 and 6 are wrong.
Look for the clue that includes the wrong digits and helps to identify correct digits - link reference technique.
Select Clue 1 as it includes two of the three incorrect digits.
Clue 1: Code 3 4 2 : One digit right but wrongly placed.
- As digits 2 and 4 are wrong, digit 3 must be the correct one.
- Its correct position must be the middle or rightmost.
- The second conclusion follows the valuable practice of extracting as much information as possible in an analysis.
Step 2: Probable position elimination to get the correct position of the single correct digit 3
Clue 2 eliminates rightmost position for 3.
Clue 2: Code 2 7 3 : One digit right but wrongly placed.
- With probable positions for correct digit 3 already curtailed to middle or rightmost (in Clue 1), Clue 2 eliminates the rightmost and the right position of the correct digit 3 is in the middle.
- The lock opening code is of the form [ ? 3 ? ].
Step 3: Deduce the correct code by positional block conflict
Clue 3 becomes the most important one as it has two digits right, both well placed.
Clue 3: Code 1 6 5 : Two digits right and are well placed.
- As middle position has already been blocked by correct digit 3, the digit 6 in the middle must be wrong, and the rest 1 and 5 are the two correct digits in right places.
- This is positional block conflict in the middle position between the block by correct digit 3 and the digit 6 occupying the blocked position in the clue.
Solution: The code to open the lock is [ 1 3 5 ].
This is easy, I suppose. Let's take up the real challenge.
Solution to the Real Puzzle Challenge: Open the 3 Digit Number Lock 342 Using the FIRST Four Clues
Alert: The solution of this variation of the puzzle involves heavy reading and patience unless the reader is experienced or inherently gifted in logic analysis and pattern based reasoning.
Ignoring Clue 5, your most potent weapon for the earlier solution, should make this puzzle variation harder to solve.
First goal is to crack open a chink in the puzzle and find at least one correct or incorrect digit.
Step 1: First hit: Identify one correct digit from Clue 3 and Clue 4
With a sharper eye for hidden patterns of a digit in more than clue, now you identify promise in Clue 3 and Clue 4 together as,
- The two have one digit 5 common.
- Both have two digits right in their hint codes - a strong promise for producing a breakthrough.
Clue 3: Code 1 6 5 : Two digits right and are well placed.
Clue 4: Code 8 5 3 : Two digits right but in wrong places.
Your reasoning:
- If digit 5 were the incorrect digit in Clue 3, lock opening code would have been of the form [ 1 6 ? ].
- The two correct digits, 3 and 8 in Clue 4 would have claimed the single free rightmost position, which would have been impossible.
- Conclusion: digit 5 must be one of the two correct digits in both the clues and its correct place is the rightmost by Clue 3.
- Lock opening code is of the form: [ ? ? 5 ].
- Assume "Something" is False (or wrong).
- Apply reasoning to conclude: the false assumption leads to a Violation of a Fundamental rule, a Contradiction, or an Impossibility.
- Decide: initial assumption of "Something" False was wrong, and the "Something" must be Right.
Step 2: Identify one of two digits as correct and a positional block
Decide to use false assumption based logic again. This time, select Clues 1 and 2 as both include the common digits 2 and 3 with both the digits' only valid position as the middle.
Clue 1: Code 3 4 2 : One digit right but wrongly placed.
Clue 2: Code 2 7 3 : One digit right but wrongly placed.
- Assume: Both the digits 2 and 3 in the two clues wrong. Logic chain:
- In Clue 1, the correct digit 4 would occupy the leftmost position (as the rightmost already blocked by correct digit 5).
- In Clue 2, the single correct digit 7 would also claim the leftmost position, leading to a conflict in leftmost position with digit 4.
- Conclusion: Both the digits 2 and 3 cannot be wrong, one of these two must be correct.
- For either of these to be correct, it would have the only correct place as the middle position. You don't know yet which of 2 or 3 is correct, but for sure the middle position is blocked by the correct one. This is a positional block, but by a pair of probable correct digits (not by a single correct digit).
Step 3. Identify the second correct digit by the positional block and crack the code
Take up the most promising Clue 3 as it has two correct digits in their right places.
Clue 3: Code 1 6 5 : Two digits right and are well placed.
- As middle position is already blocked by either of the digits 2 or 3, digit 6 in the middle is incorrect, and 1 is the second correct digit in leftmost position.
- Lock opening code is of the form: [ 1 ? 5 ].
- Remember: Either 2 or 3 is the contender for the third correct digit in the middle position.
The third correct digit 3 is revealed by elimination (or positional lockout of 8 having no place in the correct code).
Clue 4: Code 8 5 3 : Two digits right but in wrong places.
- The clue has only 3, and not 2, the second contender for the third correct digit.
- 3 is the third correct digit in the middle place - breakthrough by elimination.
- The lock opening code is: [ 1 3 5 ].
Verify the correctness of the code against unused Clue 5.
Clue 5: Code 2 6 4 : Nothing is correct.
- None of the three digits are in the correct code 135 and the code verified.
Lessons learned on logic analysis and use of reasoning techniques
Logic analysis and pattern based reasoning techniques in the easier puzzle solution using any four clues
- Strategy of identifying as many incorrect digits as possible in the first step: Adopted by using Clue 5 to identify three digits as incorrect.
- Link reference technique: A natural way to select the next clue containing an incorrect or a correct digit. Adopted when Clue 1 containing incorrect digits 2 and 4 was selected to identify the single correct digit 3.
- Extracting as much information as possible in an analysis: This is a valuable and important approach often proving to be the key to a later breakthrough. Because of curtailing the probable positions for correct digit 3 in analyzing Clue 1 in Step 1, its position could be confirmed in the next step.
- Positional block conflict: In a positive clue, when a digit occupies a position already blocked by a correct digit, it is identified as incorrect. The correct code is cracked in step 3 by positional block conflict in the middle position.
Logic analysis and pattern based reasoning techniques used in harder puzzle solution using first four clues
- False assumption based logic: This can be classified as an advanced logic analysis technique. The first breakthrough in identifying the correct digit 5 along with its correct place could be achieved by applying this technique. The logic details are repeated.
- Assume "Something" is False (or wrong).
- Apply reasoning to conclude: the false assumption leads to a Violation of a Fundamental rule, a Contradiction, or an Impossibility.
- Conclude: initial assumption of "Something" False was wrong, and the "Something" must be Right.
- Positional block: Arises when a position in the code is reserved by one or more than one candidate for a correct digit. In step 2, Clues 1 and 2 provided the breakthrough middle position block by first identifying one of 2 or 3 to be right and then reserving the middle position by one of the two.
- Positional lockout: This is a rarer variation of positional block when all three positions in the correct code become invalid for a digit in a clue. This identifies the digit as wrong. In the last step of the solution, though the code could be cracked by digit elimination, the single incorrect digit 8 in Clue 4 also suffered from positional lockout, further confirming its incorrectness.
The solutions of this puzzle provide a rich collection of lessons in advanced logic analysis and pattern based reasoning.
Overall, it has been an exercise of choosing the most suitable combination of clues individually or together for the series of breakthroughs following a strategic approach.
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