Crack Number Lock Puzzle 016 in Three Steps

Crack number lock puzzle 016 in three steps from 5 clues each with a 3 digit code and statement on digit and position correctness on the hint code.

The Number Lock Puzzle with 016: Clues

Following are the five clues:

Clue 1. Code 4 0 3: Two digits are correct and in the right places.

Clue 2. Code 3 0 4: Two digits are correct — 1 in the right place and 1 in the wrong place.

Clue 3. Code 3 5 0: Two digits are correct but both wrongly placed.

Clue 4. Code 3 1 2: Two digits are correct but both wrongly placed.

Clue 5. Code 0 1 6: Two digits are correct but both wrongly placed.

Find the code to open the number lock in three analytical steps.

Time to solve 10 minutes.

Hints: Scan all clues. Find clues with breakthrough patterns in common digits.

Solution to Crack Number Lock Puzzle 016 in Three Steps

3 is the most commonly occurring digit in the clues. Assuming it false in selected pair of clues should provide the first breakthrough.

Step 1. False assumption logic identifies first correct digit

Clue 3. Code 3 5 0: Two digits are correct but both wrongly placed.

Clue 4. Code 3 1 2: Two digits are correct but both wrongly placed.

• Clues 3+4: Assume 3 wrong → 4 correct digits (5,0,1,2) in a three digit code → impossibility → 3 right.

Step 2. Positional correctness analysis produces second correct digit

Clue 1. Code 4 0 3: Two digits are correct and in the right places.

Clue 2. Code 3 0 4: Two digits are correct — 1 in the right place and 1 in the wrong place.

• Clues 1+2: Clue 1: correct position of 3 rightmost; in Clue 2, its position is wrong, only 0 satisfies in both to be correct and in place, not 4 (in positional conflict with 3 in rightmost) → partial code [ ? 0 3 ].

Step 3. Fix the third correct digit by positional correctness analysis and no contradiction rule

Clue 4. Code 3 1 2: Two digits are correct but both wrongly placed.

Clue 5. Code 0 1 6: Two digits are correct but both wrongly placed.

• Clue 4+5: 3 and 0 are right but wrongly placed → one of 1, 2 or 6 is the second correct digit in leftmost secret code position.
• 2 or 6 violates Clue 5 or Clue 4, respectively:
• 2 produces code 203 → violates Clue 5 hint code (016) with only one common correct digit 0.
• 6 produces code 603 → violates Clue 4 hint code (312) with only one common correct digit 3.
• Only 1, the digit common to both clues, if correct, satisfies both the clues with no contradiction → 1 is the third correct digit in leftmost position → Secret code [ 1 0 3 ].

Test: satisfies all clues. Answer 103. Verify yourself.

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Lessons Learned

1. Common Digits Are Logical Anchors:

• Digit 3 appears in four clues, and the clues with 3 analyzed  together should provide the breakthrough.

False assumption logic: False Assumption + Contradiction = Proof of correctness.

• In Clues 3 and 4, Assuming "3 is wrong" led to four correct digits (5,0,1,2)— impossible in a 3 digit code. This contradiction proves 3 must be correct.

Positional Correctness Analysis in a Pair of Clues:

• In Clue 1, correct position of 3 rightmost but in Clue 2, its position is wrong. Only 0 satisfies both clues to be correct and in place, not 4 (in positional conflict with 3).
• A second breakthrough by this approach of analyzing a pair of clues 4 and 5: with correct digits 0 and 3 common in the two clues, only the common digit 1 could satisfy both clue condition with no contradiction. Other two: both 2 and 6 produced contradictions if correct.

Positional conflict is a frequently used pattern for breakthroughs.

• In Clue 2, digit 4 suffered a direct positional conflict with digit 3 already  occupying rightmost position proving second probable 0 to be correct and in position.

Chain Reasoning, Not Guessing.

• Each deduction feeds into the next:
• Step 1. Use Clues 3+4 to prove 3 is correct using false assumption logic on common digit 3.
• Step 2. Use Clue 1+2 to confirm rightmost position for 3, digit 4 suffered positional conflict → 0 takes middle position.
• Step 3. Clues 4+5: apart from correct digits 0 and 3, only common digit 1 could be considered as the second correct digit not contradicting the clues.

All logic in structured progression.

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

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