Crack the number lock puzzle 048 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 048: Clues
You are given the following five clues to deduce the correct 3 digit code:
Clue 1: Code 0 4 8: Two digits correct both wrongly placed.
Clue 2: Code 2 5 4: Two digits are correct and both are in the right places.
Clue 3: Code 5 8 2: Two digits are correct — 1 in the right place and 1 in the wrong place.
Clue 4: Code 8 0 4: Two digits are correct — 1 in the right place and 1 in the wrong place.
Clue 5. Code 9 8 4: Two digits are correct and in the right places.
Find the code to open the number lock in three analytical steps.
Time to solve 15 minutes.
Hints: Go through all the clues first carefully, searching for promising patterns of common digits in the clues. For quick solution in assured steps, such patterns in multiple clues have to be exploited for step by step breakthroughs.
Solution to Crack the Number Lock Puzzle 048 in Three Steps
4 and 8 are the most commonly occurring two digits. Explore correctness of the two.
Step 1. Find the first correct digit by false assumption logic applied on a suitable promising digit
4 being the most frequent common digit we'll apply the breakthrough technique of false assumption logic on 4 first taking Clues 2 and 5 together.
Clue 2. Code 2 5 4: Two digits are correct and both are in the right places.
Clue 5. Code 9 8 4: Two digits are correct and in the right places.
- Assume 4 wrong.
- If 4 is wrong, from Clue 2, partial code: [ 2 5 ? ] and from Clue 5, [ 9 8 ? ] → contradiction → 4 correct → partial code [ ? ? 4 ]. Also, if 4 is wrong, four digits (2,5,9,8) are to be correct in a three digit code → an impossibility → 4 correct.
Step 2. Find the second correct digit from clues with 4 and two other common digits
Using the common occurrence of correct digit 4 in Clues 1 and 4 (link reference technique), both stating wrongly placed digits, analyze which of the other two common digits 0 or 8 is correct.
Clue 1. Code 0 4 8: Two digits correct both wrongly placed.
Clue 4. Code 8 0 4: Two digits are correct — 1 in the right place and 1 in the wrong place.
- Combined Clue Pair Analysis on Positional Correctness: If 0 is correct, it is wrongly placed in both and its position in the secret code is rightmost, already occupied by 4 → it is locked out with no place in the code → 0 is incorrect → 8 is the second correct digit in the middle (supported directly by Clue 5 as well) → partial code [ ? 8 4 ].
Step 3. Find the third correct digit by positional conflict
This step is easy as Clue 2 reveals the incorrect digit by positional conflict.
Clue 2. Code 2 5 4: Two digits are correct and both are in the right places.
- Probable second correct digit in the clue 5 (apart from 4) is in direct positional conflict with 8 in the middle of the partially formed secret code.
- 5 is incorrect and 2 is correct in its correct place in the secret code.
Solution: Lock opening code is [ 2 8 4 ].
Verify the secret code solution against all the clues. It is a good practice to double-check, and it takes just a little time more.
Clue 1. Code 0 4 8: Two digits correct both wrongly placed. (correct code 284)
- Both correct code digits 4 and 8 are indeed wrongly placed in the hint code 048. Secret code verified.
Clue 2. Code 2 5 4: Two digits are correct and both are in the right places. (correct code 284)
- Both correct code digits 2 and 4 are indeed correctly placed in the hint code 048. Secret code verified.
Clue 3. Code 5 8 2: Two digits are correct — 1 in the right place and 1 in the wrong place. (correct code 284)
- Correct code digit 8 is in its correct position, and second correct digit 2 is wrongly placed as required in the clue. Secret code verified.
Clue 4. Code 8 0 4: Two digits are correct — 1 in the right place and 1 in the wrong place. (correct code 284)
- Correct code digit 4 is in its correct position, and second correct digit 8 is wrongly placed as required in the clue. Secret code verified.
Clue 5. Code 9 8 4: Two digits are correct and in the right places. (correct code 284)
- Both correct code digits 8 and 4 are in their correct positions as required in the clue. Secret code verified.
Secret code [ 2 8 4 ] satisfies all the clues.
Solution Outline (Concise Version)
Leverage the pattern of digit 4 common to four clues. Apply false assumption logic on 4 in suitably chosen pair of clues.
Step 1: Analyze most promising positive Clues 2 and 5 having digit 4 common in the same position.
- Clue 2 (2 5 4) + Clue 5 (9 8 4), two digits right in right positions in both — Assume 4 is wrong → leads to four correct digits (2, 5, 9, 8); also creates two conflicting partial codes [ 2 5 ? ] and [ 9 8 ? ] → contradiction → 4 must be correct in its rightmost position → either (2,8) or (5,9) correct in their correct positions → partial code [ ? ? 4 ].
Step 2: Leverage Combined Clue Pair Analysis on Positional Correctness of Clues 1 and 4, both including correct digit 4 and two more digits common to both.
- Clue 1 (2 5 4) + Clue 4 ( 8 0 4), If 0 is correct, it is wrongly placed in both and is in positional conflict with correct digit 4 → it is locked out with no place in the code → it is incorrect → 8 is the second correct digit in the middle → partial code [ ? 8 4 ].
Step 3: Look for positional conflict in either middle or rightmost and discover it in Clue 2.
- Clue 2 ( 2 5 4 ): Two digits are correct and in the right places → 5 is the second correct digit in a position reserved by 8 → positional conflict → 2 is the correct digit, second in the clue and third in the secret code [ 2 8 4 ].
Lessons Learned
- Common Digits Are Logical Anchors:
- Digit 4 appears in four clues and 8 in three clues. Recurrence of 4, especially in the same position, makes it a prime candidate for combined clue analysis. Always group clues by common digits.
- In Clues 3 and 4, Assuming "4 is wrong" led to four correct digits (2,5,9,8)— impossible in a 3 digit code. This contradiction proves 4 must be correct — a powerful logical tool. This also confirms its position at the rightmost.
- Analyze Clues 1 and 4, both include correct digit 4 and two more digits common to both. 0 common to both cannot be correct because it would need to be in rightmost place — but 4 already occupies it. Digit 8 is identified as the second correct digit in this process. Positional logic is often the key to an important breakthrough.
- In Clue 5, digit 5 suffered a direct positional conflict with digit 8 already occupying middle position providing the final breakthrough.
- Each deduction feeds into the next:
- Step 1. Use Positive Clues 2+5 to prove 4 is correct → fix its position → 4 takes rightmost position.
- Step 2. Use Clue 1+4 to confirm 0 incorrect and eliminated to confirm 8 correct → 8 takes middle position.
- Step 3. Identify Clue 2 to reveal 5 in positional conflict with 8 in middle → 5 eliminated confirms 2 in its position.
All logic in structured progression.
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