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 shows 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.

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Solution to the Number Lock Puzzle 829 in Easy Steps

Observations and goal: 

• The three sets of clues with maximum-frequency digit 2, digit 1 and digit 9 shared by the groups of clues should make a step-by step solution easy to reach.

• Objective of the solution is to make it as easy to follow as possible.

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

Reason for clue choice: Clues 1, 4 and 5 have 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 => Violation proves assumption wrong and 2 correct.

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

• Partial secret code [ ? ? 2 ].

Step 2. Leveraging Common Digits to Get Second Correct Digit

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 for applying false assumption to identify the correct digit.

• 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.

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 => 1 correct.

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

• 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: 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 => assumption wrong => 9 third correct digit.

Step 4: Finalizing Positions of 1 and 9 by Positional Analysis of Digits

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:

• 1 is the correct digit wrongly placed because rightmost position is already occupied by 2 in partial code [ ? ? 2 ] => 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: 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, proving the digit 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 definitively.

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.

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