Given five clues, each with a 5 digit code and hints on correct digits and their placements, can you find the correct code from the clues to open the lock?
The 5 digit number lock puzzle
Find the 5 digit code from the five clues to open the number lock:
Clue 1: Code 1 4 6 7 3 : Four digits right, one in correct position.
Clue 2: Code 0 2 6 3 7 : Three digits correct and all rightly placed.
Clue 3: Code 6 9 3 0 8 : One digit right, but in wrong position.
Clue 4: Code 5 6 0 7 3 : Two digits correct both wrongly placed.
Clue 5: Code 5 9 4 1 8 : Two digits correct one rightly placed.
Take your time. This is not an easy number lock riddle.
Solution to the 5 digit number lock puzzle
On analysis of the five clues it is clear,
- Tentative conclusion 1: Clue 1 is the most important (as it has the potential to identify four correct digits at one go).
- Tentative conclusion 2: Identifying the right digit in right place in Clue 1 should give us the critical breakthrough. It is the first goal.
- Tentative conclusion 3: Clue 2 is the second most important one (as it refers to three right digits in their right places).
First breakthrough
Analyze Clues 1 and 2 first:
Clue 1: Code 1 4 6 7 3 : Four digits right, one in correct position.
Clue 2: Code 0 2 6 3 7 : Three digits correct and all rightly placed.
From Clue 1 and Clue 2, it seems at first, digit 6 is a correct digit in its right place, but what if say, digit 1 is correct in Clue 1 and is in its right position! The logic in favor of digit 6 is not foolproof.
Assumed condition: digit 6 is the single wrong digit in Clue 1:
Clue 1: Code 1 4 6 7 3 : Four digits right, one in correct position.
- Conditional conclusion 1: Digits 1, 4, 7 and 3 are correct and one of these is rightly placed.
We will analyze the candidature of these four digits for the single right digit in right place in Clue 1.
Take Clue 5:
Clue 5: Code 5 9 4 1 8 : Two digits correct one rightly placed.
If either of digits 1 or 4 were in its right place in Clue 1, in Clue 5 both cannot appear in very different places.
- Conditional conclusion 2: Digits 1 or 4, even if correct, is not in its right place in Clue 1.
- Conditional conclusion 3: Single right place right digit candidate is either 3 or 7.
Take up Clue 1 and Clue 2 to evaluate digits 3 and 7 for their candidature:
Clue 1: Code 1 4 6 7 3 : Four digits right, one in correct position.
Clue 2: Code 0 2 6 3 7 : Three digits correct and all rightly placed.
If either of digits 3 or 7 were the single right digit in its right place, it violates placements of both in Clue 2.
- Conclusion 1: None of the four digits other than 6 in Clue 1 can be the single right digit in its right place.
- Conclusion 2: Digit 6 is the right digit in its right 3rd place in Clue 1.
This is the critical breakthrough based on exhaustive logic.
Identifying incorrect and correct digits
In which other clue digit 6 appears in a promising role? Clue 3 is the choice:
Clue 3: Code 6 9 3 0 8 : One digit right, but in wrong position.
Right digit 6 satisfies the conditions of the clue.
- Conclusion 3: Digits 9, 3, 0 and 8 all four digits are incorrect. A very fruitful outcome.
With digit 3 identified as incorrect, immediate gains from Clue 1:
Clue 1: Code 1 4 6 7 3 : Four digits right, one in correct position.
- Conclusion 4: Digits 1, 4, 6 and 7 are the four correct digits and digit 6 is in its correct position of 3rd from left. Again a very fruitful outcome.
In which clue more than one of these correct digits appear together and are described as only correct digits? Clue 5 is the choice:
Clue 5: Code 5 9 4 1 8 : Two digits right, and one rightly placed.
- Conclusion 5: Digits 1 and 4 being already identified as correct, digit 5 must be incorrect. Five digits 9, 3, 0, 8 and 5 are incorrect.
- Conclusion 6: Only remaining digit 2 must be the fifth correct digit. Digits 1, 4, 6, 7 and 2 are correct.
- Conclusion 7: 3rd or 4th place is for either of digit 1 or 4.
Identifying places of the correct digits
At this point, Clue 2 becomes the most important one:
Clue 2: Code 0 2 6 3 7 : Three digits correct and all rightly placed.
- Conclusion 8: Digits 2, 6 and 7 are the right digits in right positions.
- Conclusion 9: Lock opening code is of the form ? 2 6 ? 7. Only first and fourth places are free for the remaining two digits 1 and 4.
Analyze Clue 1 and Clue 5 together as digits 1 and 4 appear in both.
Clue 1: Code 1 4 6 7 3 : Four digits right, one in correct position.
Clue 5: Code 5 9 4 1 8 : Two digits right, and one rightly placed.
In Clue 1, positions of both 1 and 4 are wrong, but in Clue 5, 3rd or 4th position is the correct position for either of the digits 1 or 4.
1st position is wrong for digit 1 and 3rd position already taken up. So,
- Final conclusion: Digit 1 can take up the only free position 4th from left, and 1st position goes to digit 4.
The code to open the 5 digit lock is: 4 2 6 1 7.
Clue 4 remains unused. This indicates the solution to be an efficient one, if not the most efficient with bulletproof logic.
Verify the correctness of the code by tallying the code with each of the five clues.
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