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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