Challenge: Solve Number Lock Puzzle 143 in Quick Logic Analysis

Submitted by Atanu Chaudhuri on Sun, 28/09/2025 - 16:59

Can you solve number lock puzzle 143 in a quick series of breakthroughs? Each clue shows hint code and digit-position correctness.

3 Digit Number Lock Puzzle With 143 in Hint Codes

Following are the five clues as hints:

Clue 1: Code 1 4 3: One digit is correct but in the wrong place.

Clue 2: Code 6 1 9: Two digits are correct but both are in the wrong places.

Clue 3: Code 2 7 5: One digit is correct and in the right place.

Clue 4: Code 9 0 3: One digit is correct and in the right place.

Clue 5: Code 8 1 6: One digit is correct in the wrong place.

Find the number lock code from the clues.

Time to solve: 10 minutes.

Solution to Solve Number Lock Puzzle 143 in Quick Logic Analysis

This puzzle is already solved in a solution that involves deeper logic analysis. I will present a simpler logic based solution now.

Solution comprising three breakthroughs in succession is based on common digit correctness and position patterns in multiple clues.

Step 1. First breakthrough by position and correctness conflict

Clue choice and digit pattern:

Clues 1 and 4 have 3 common with conflicting position descriptions.

Clue 1: Code 1 4 3: One digit is correct but in the wrong place.
Clue 4: Code 9 0 3: One digit is correct and in the right place.

Logic analysis:

Clues 1+4: 3 wrong by position and correctness conflict.
Reason: 3 is a correct digit candidate, it occupies the same rightmost position in both clues, but a correct digit cannot be in its correct position in one clue and wrongly placed in the other. This creates the conflict.

Need to leverage this erroneous digit to achieve next breakthrough to identify correct digits in right positions.

Step 2. Second breakthrough by false assumption on common digit 1 in multiple clues

Clue choice and digit patterns:

Clues 1, 2 and 5 have 1 common. False assumption of 1 wrong creates violation of Clue 3.

How: With 3 erroneous in Clue 1, the clue code 143 lends an opportunity to choose a single digit out of two (a binary situation) for correctness test. This is fertile ground for applying false assumption logic on correctness of one of the two.

Clue 1: Code 1 4 3: One digit is correct but in the wrong place.
Clue 2: Code 6 1 9: Two digits are correct but both are in the wrong places.
Clue 5: Code 8 1 6: One digit is correct in the wrong place.
Clue 3: Code 2 7 5: One digit is correct and in the right place.

Logic analysis:

Clues 1+2+5: False assumption: Assume 1 wrong => 4 correct in Clue 1=> 6 and 9 correct in Clue 2 and you get three correct digits 4, 6 and 9.
But, none of three correct digits 4, 6 and 9 appears in Clue 3 => Violates Clue 3 and it proves "1 wrong" is a false assumption leading to confirmation of 1 as the first correct digit.
Wrong position exclusion: 1 is wrongly placed (leftmost) in Clue 1 (1 4 3) and wrongly places (middle) also in Clue 2 (6 1 9). 1 is left with its only valid position rightmost => partial secret code [ ? ? 1 ].
With 1 the only correct digit in Clue 5, digits 6 and 8 wrong => with 6 wrong, 9 is the second right digit in middle or leftmost position in Clue 2 (6 1 9) => partial secret code [ ? 9 1 ] or [ 9 ? 1]. 9 cannot be in rightmost already claimed by 1.

With the correct digit 1 identified, its position confirmed, and with digits 6 and 8 from Clue 5 now known to be incorrect, we have extracted all necessary information from Clues 1 and 5 for now.

Next choice of the clues: Combined analysis of Clues 2, 3 and 4 for the final breakthrough.

Step 3. Third breakthrough by positional analysis and position conflict

Clue choice: Clues 3 and 4 in combination. Clue 2 won't be needed.

Patterns: Clue 4 confirms position of 9. The last correct digit identified from Clue 3 by positional conflict.

Clue 3: Code 2 7 5: One digit is correct and in the right place.
Clue 4: Code 9 0 3: One digit is correct and in the right place.

Logic analysis:

Clue 4: 9 in leftmost position and 1 in rightmost => Clue 4: both 2 and 5 in Clue 3 wrong by positional conflict claiming already claimed positions => 7 third correct digit in the middle.
Solution: Secret code [ 9 7 1 ].

All clues are used in the analytical solution. No further verification needed.

If you wish, verify the secret code 971 against all five clues.

Key Strategies You Learned:

1. Position and correctness conflict: When the same digit in same position is stated as probable "correct" in two clues but "wrongly placed" in one and "correctly placed" in the other, the conflict confirms the digit as incorrect.

Ex: Digit 3 in Clues 1 (position rightmost, wrongly placed) and 4 (position rightmost, correctly placed) must be wrong.

2. False assumption violating a third clue: In two clues, assumption of a common digit wrong violates a third clue by the formation of a secret code with three digits none of which appear in the third clue.

Ex: With assumption of 1 wrong in Clues 1 and 2 leads to three correct digits 4, 6 and 9 in the secret code none of which appears in Clue 3, proving the assumption wrong and 1 right.

3. Position analysis — Position confirmation by exclusion: Two positions for the correct digit in two clues stated to be wrong, confirms the remaining position correct for the digit.

Ex: In both Clue 1 (1 4 3) and Clue 2 (6 1 9), position of correct digit 1 is stated wrong. This leaves the remaining rightmost position for 1.

4. Positional Conflict: Once a digit's correct position in secret code is confirmed, it creates a positional claim. Any other digit claiming that same position in a subsequent clue must be incorrect.

Ex: With 1 confirmed in rightmost position and 9 leftmost of secret code, the digits 2 and 5 claiming the same positions in Clue 3 (hint code 275) must be incorrect.

5. Correct digit by incorrect digit elimination: Elimination of incorrect digits in a clue confirms the remaining digit as correct.