Solve Number Lock Puzzle 829 in a Few Simple Steps

Can you crack number lock puzzle 829 in a few simple steps using 5 clues? Each clue describes hint code and digit-position correctness.

3 Digit Number Lock Puzzle With 829 in Hint Codes

Clue 1: Code 8 2 9: Two digits are correct but both are in the wrong places.

Clue 2: Code 6 9 1: Two digits are correct — 1 in the right place and 1 in the wrong place.

Clue 3: Code 2 0 3: One digit correct in wrong place.

Clue 4: Code 5 2 1: Two digits are correct but both are in the wrong places.

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

Time to solve: 15 minutes.

---

Solution to the Number Lock Puzzle 829 in Easy Steps

Observations, patterns and goal: 

• Pattern and use: Three sets of clues with common digit 2, digit 1 and digit 9 are shared by the groups of clues. This should make a step-by step solution easy to reach.

• Pattern and use: All clues are positive clues with clue code digits described correct. Positive clues are helpful in breakthroughs when analyzed together.

• Objective: The solution should be as easy to follow as possible.

Step 1: Find a Correct Digit by Contradiction Created by False Assumption

Reason for clue choice: Clues 1, 4 and 5 have digit 2 common and are positive clues with one or two digits stated correct. This is a promising situation for breakthroughs.

• Clue 1: Code 8 2 9: Two digits are correct but both are in the wrong places.

• Clue 4: Code 5 2 1: Two digits are correct but both are in the wrong places.

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

Analysis:

• Clues 1+4: Assume digit 2 wrong => 8 and 9 are two correct digits in Clue 1 (8 2 9) and 5 and 1 are the two correct digits in Clue 4 (5 2 1).

• => Four digits (8, 9, 5, 1) correct.

• => Impossible for a 3 digit code.

• => Contradiction proves assumption wrong and 2 correct.

• Clue 5: Digit 2 gets its correct rightmost position.

• Partial secret code [ ? ? 2 ].

Step 2. Leverage Common Digits to Get Second Correct Digit

Clues chosen for breakthrough analysis:

• Clue 2: Code 6 9 1: Two digits are correct — 1 in the right place and 1 in the wrong place.

• Clue 4: Code 5 2 1: Two digits are correct but both are in the wrong places.

Reasons for clue choice:

• Clues 2 and 4 share common digit 1.

• Both are positive clues with two digits stated correct.

• This pattern is ideal to apply false assumption logic on common digit 1 to identify the second correct digit.

Analysis:

• Assume common digit 1 wrong => 6 and 9 correct in Clue 2, and 5 and 2 correct in Clue 4 => four digits (2, 5, 6, 9) correct => Impossible in a 3 digit number lock => Assumption wrong and 1 correct.

Step 3. Last Correct Digit Using Common Digit Pattern in Clues 1 and 2

Clues chosen:

• Clue 1: Code 8 2 9: Two digits are correct but both are in the wrong places.

• Clue 2: Code 6 9 1: Two digits are correct — 1 in the right place and 1 in the wrong place.

Analysis: Promising pattern is 9 shared by the positive clues both stating two digits correct.

• Assume 9 wrong => 2 and 8 right in Clue 1, and 1 and 6 right in Clue 2 => four digits (1, 2, 6, 8) right in a 3 digit number lock => Violation of puzzle conditions proves assumption wrong and 9 the third correct digit.

Step 4: Finalizing Positions of 1 and 9

Clue 2 includes both 1 and 9 in its hint code:

• Clue 2: Code 6 9 1: Two digits are correct — 1 in the right place and 1 in the wrong.

Positional analysis to spot positional conflict:

• 1 is the correct digit wrongly placed because rightmost position is already occupied by 2 in partial code [ ? ? 2 ]. This is positional conflict between 2 and 9.

• => 9 is the second correct digit in its correct middle place in both the clue code and the secret code.

• => 1 takes the vacant leftmost position.

Final Secret Code: [ 1 9 2 ]

Verification:

• Clue 1: 8 2 9 => 9 (correct, wrong place), 2 (correct, wrong place) => Matches "Two digits correct, both wrong places". Correct.

• Clue 2: 6 9 1 => 9 (correct, right place), 1 (correct, wrong place) => Matches "Two digits correct — 1 right place, 1 wrong place". Correct.

• Clue 3: 2 0 3 => 2 (correct, wrong place) => Matches "One digit correct in wrong place". Correct.

• Clue 4: 5 2 1 => 2 (correct, wrong place), 1 (correct, wrong place) => Matches "Two digits correct, both wrong places". Correct.

• Clue 5: 4 7 2 => 2 (correct, right place) => Matches "One digit correct and in right place". Correct.

All clues are satisfied.

Key Strategies You Learned:

1. Proof by Contradiction using False assumption logic: Assume a key digit is wrong. If this leads to an impossible situation (like requiring four correct digits), the assumption is false. This proves the digit assumed wrong must be correct.

2. Leveraging High-Frequency Digits: A digit appearing across multiple clues is a prime candidate for testing via contradiction to establish its correctness with certainty.

3. Positional analysis: Use the fixed position of a digit in the partial code to interpret the "right/wrong place" information in other clues, resolving the final positions of other correct digits.

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

---

Puzzles you may enjoy

Easy to hard brain teasers with systematic solutions:

Challenging brain teasers with solutions: Long list.

---