Can You Crack Number Lock Puzzle With Hint Code 513 Many Ways?

Submitted by Atanu Chaudhuri on Thu, 21/08/2025 - 15:38

Crack Number Lock Puzzle With Hint Code 513 Many Ways

Can you crack number lock puzzle with hint code 513 in more than one way? The puzzle offers 5 clues each with hints on code digits and placements.

The Number Lock Puzzle With Hint Code 513 In Its Clues

Clue 1. Code 5 1 3: No digit is correct.

Clue 2. Code 3 7 6: Two digits are correct — 1 in the right place and 1 in the wrong place.

Clue 3. Code 8 5 9: One digit is correct but in the wrong place.

Clue 4. Code 9 6 0: Two digits are correct but both are in the wrong places.

Clue 5. Code 6 7 8: Two digits are correct but both are in the wrong places.

Find the solution to the puzzle with and without using the no-digit-is-correct clue.

Time to solve: 20 minutes.

Hints: This is a two-in-one puzzle. The first puzzle using the all-incorrect Clue 1 might be easier and to be solved first. The experience gained should help in solving the second harder puzzle.

Use the common digit patterns in multiple clues to identify incorrect and correct digits.

First Solution to Crack Number Lock Puzzle With Hint Code 513 in its Clues Using All the Clues

First step objective must always be to identify a correct or an incorrect digit.

Step 1. Identify correct digits using information on incorrect digits

Clues 1 and 2 together identify two digits as correct.

Clue 1. Code 5 1 3: No digit is correct.

Clue 2. Code 3 7 6: Two digits are correct — 1 in the right place and 1 in the wrong place.

Incorrect 3 from Clue 1 identifies both 6 and 7 as correct.

Step 2. Identify the correct places of the two correct digits

Clues 2 and 5 both have the two correct digits 6 and 7 common. In addition, Clue 4 with digit 6 along with the first two should produce the correct places of 6 and 7.

The clues with one or more than one common digits analyzed together invariably produce a breakthrough.

Clue 2. Code 3 7 6: Two digits are correct — 1 in the right place and 1 in the wrong place.

Clue 4. Code 9 6 0: Two digits are correct but both are in the wrong places.

Clue 5. Code 6 7 8: Two digits are correct but both are in the wrong places.

Assume 7 is the correct digit in its correct place in Clue 2. Then, the second correct digit 6 must be the leftmost. But by Clue 5, leftmost is the wrong place for 6. The correct digit 6 is effectively locked out of the code and thus proves the original assumption wrong. This is false assumption based logic analysis.

Conclusion: 6 must be the correct digit in its rightmost position in Clue 2 with 7 taking up the leftmost position, as it is the second correct digit wrongly placed.

Partially formed lock opening code is [ 7 ? 6 ].
Additional information: digit 8 is incorrect in Clue 2.
This is maximum information extraction in an analytical step that helps in later breakthroughs.

Analysis of even the three clues couldn't help to choose between 0 and 9 as the third correct digit in Clue 4.

Step 3. Finding the third correct digit to crack the code

Clue 3 includes incorrect digit 8 and the candidate correct digit 9 in a wrong position. Additional promise is in the third digit 5 facing a positional lockout.

Clue 3. Code 8 5 9: One digit is correct but in the wrong place.

Digit 8 wrong (from step 2), and digit 5 is locked out of the code and so is incorrect. None of the three positions right for 5 because of the partially formed code [ 7 ? 6 ] and its wrong position clue description.

Conclusion: Digit 9 must be the third correct digit in the middle, the two digits in the clue eliminated.

Lock opening code is [ 7 9 6 ].

Despite using the most powerful resource of the all digits wrong clue, it took three steps to crack the code.

Lessons from the solution

Strategy of identifying maximum number of correct digits by analyzing multiple clues together:

In Clue 1 and 2, two correct digits are identified in one step.

Use of all clues with correct digits common increases chances of a breakthrough. This is use of link reference technique to the extreme.

Analyzing the three Clues 2, 4 and 5 with one or both the correct digits common helped to fix the positions of the two correct digits 6 and 7.

False assumption based logic analysis of assuming digit 7 correct in correct position in Clue 2 caused the second correct digit 6 locked out of the code (with no place in the code even when it is the second correct digit) when all three clues are considered together. The positional lockout established the original assumption as wrong and digit 6 to be the correct digit in its rightmost correct place.
Positional constraint: With rightmost position blocked by 6, the correct place for digit 7 was fixed as the leftmost.
Partial code formation helps: Forming the partial code as [ 7 ? 6 ] helped to block the two positions for the final breakthrough.
Maximum information extraction in an analysis: Additional information of digit 8 wrong in step 2 helped in identifying the third correct digit in step 3.
Positional lockout:

In Clue 3, with digit 8 wrong and digit 5 locked out of the code by the partially formed code (and so incorrect), the remaining digit 9 is identified as the third correct digit for the middle position.

Second Solution to Crack Number Lock Puzzle With Hint Code 513 Without the All-incorrect Clue

In the last four clues, the most promising common digit is 6 in Clues 2, 4 and 5.

Clue 2. Code 3 7 6: Two digits are correct - 1 in the right place and 1 in the wrong place.

Clue 4. Code 9 6 0: Two digits are correct but both are in the wrong places.

Clue 5. Code 6 7 8: Two digits are correct but both are in the wrong places.

In Clues 4 and 5, if digit 6 is incorrect, four digits 0, 7, 8 and 9 must be correct - an impossibility. So, digit 6 must be correct.
If 6 is correct and wrongly positioned in Clue 2, its position must be the middle or the leftmost. This violates position descriptions of 6 in Clues 4 and 5.

Conclusion: Digit 6 must be correct in correct rightmost position in Clue 2.

If 7 is incorrect in Clues 2 and 5, the lock opening code is [ 8 3 6 ]. This violates Clue 4 as none of 8 or 3 is in Clue 4 hint code 960. So digit 7 must be the second correct digit. This is false assumption based logic analysis.
Partially formed code: [ 7 ? 6 ].
Additional information: Digit 8 wrong in Clue 5.

Rest of the reasoning is based on analysis of Clue 3 in the same way as the first solution.

Solution: Lock opening code [ 7 9 6 ].

The two solutions embody the spirit of Many ways technique. It pushes you always towards discovering new ways to think, new ways to reach a solution to a problem. Among many advantages of this approach, the most important is: continuous urge to find a new alternate way enhances your brain functions like no other activity. This forms a cornerstone of such a lofty idea as Natural intellect farming, no less.

Question: Which of the two solutions would you think as the easier?

However involved the logic analysis might be, ultimately, it is based on position and correctness descriptions of digits common to multiple clues.

To enjoy solving many more such number lock puzzles, click here.