Crack inventive number lock puzzle 408 in minimum steps from 5 clues each with a 3 digit code and statement on digit and position correctness of hint code.
3 Digit Inventive Number Lock Puzzle Including Hint Code 408
Following are the five clues:
Clue 1. Code 4 0 8: Two digits correct both wrongly placed.
Clue 2. Code 7 3 0: One digit right but wrongly placed.
Clue 3. Code 0 2 4: Two digits are correct — 1 in the right place and 1 in the wrong place.
Clue 4. Code 4 9 1: One digit right but wrongly placed.
Clue 5. Code 6 4 2: One digit right correctly placed.
Find the code to open the number lock in minimum steps.
Time to solve 15 minutes.
Hints: First go through all the clues 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 effectively used for step by step breakthroughs.
Step-by-Step Solution to Crack Inventive Number Lock Puzzle 408 in Three Steps
4 appears in four clues. Explore correctness of 4 analyzing a pair of clues to get a contradiction.
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. Suitable clues with 4 in hint codes will be analyzed (the chosen pair of clues should be "two digits correct" category).
Clue 1. Code 4 0 8: Two digits correct both wrongly placed.
Clue 3. Code 0 2 4: Two digits are correct — 1 in the right place and 1 in the wrong place.
Clue 4. Code 4 9 1: One digit right but wrongly placed.
Clue 5. Code 6 4 2: One digit right correctly placed.
- Assume 4 wrong.
- In Clue 1, digits 0 and 8 right and in Clue 3, digits 0 and 2 right → Essentially, the three correct digits in the code are, 0, 2 and 8 none of which appears in the hint code 491 of Clue 4 → Contradiction → 4 correct.
- From Clue 5 position of 4 is in the middle → Partial secret code: [ ? 4 ? ].
Step 2. Identify the second correct digit and its position by positional conflict
Link reference technique and digit pattern in the clue identifies the next promising clue (should be a "two digits correct" clue that includes already correct digit).
Clue 3. Code 0 2 4: Two digits are correct — 1 in the right place and 1 in the wrong place.
- 4 correct in wrong place, probable correct digit 2 conflicts with 4 in middle position and so is wrong → 0 correct on leftmost position → Partial secret code: [ 0 4 ? ].
Step 3. Find the elusive third digit by Property Change Analysis Inventive Technique
All clues satisfied the partial secret code without revealing the new third digit for the rightmost place. What then is the elusive third right digit?
What did we assume for granted? This is where awareness of inventive technique of Property Change Analysis becomes important.
Property Change Analysis Technique
When faced with a stalemate situation while solving a problem with no solution in sight,
- List out ALL the properties of the principal actor in the problem. In this problem, the principal ACTOR is a digit.
- Think hard, did you miss any property of the digits used? Did you take any aspect of the digit analysis in the clues for granted?
This focus on a single issue reveals the breakthrough answer:
- Yes, you have assumed that only the digits mentioned in the clues will form the secret code.
- Breakthrough idea: But can't there be a single digit not included in any of the hint codes?
- Act to test: Enumerate all digits used in the five clues: Wrong digits 2, 6, 1, 9, 3, 7, 8; right digits 0, 4 - total 9. But, there are 10 digits - the elusive digit 5 is missing in the clues. That must be the third correct digit in the secret code satisfying all the clues and opening the lock.
Secret code: [ 0 4 5 ].
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 4 0 8: Two digits correct both wrongly placed. (correct code 045)
- Both correct code digits 4 and 0 are indeed wrongly placed in the hint code 045. Secret code verified.
Clue 2. Code 7 3 0: One digit right but wrongly placed. (correct code 045)
- Right digit 0 occupies a wrong place in the hint code. Secret code verified.
Clue 3. Code 0 2 4: Two digits are correct — 1 in the right place and 1 in the wrong place. (correct code 045)
- Correct digit 0 is in its correct position, and second correct digit 4 is wrongly placed as required in the clue. Secret code verified.
Clue 4. Code 4 9 1: One digit right but wrongly placed. (correct code 045)
- Correct code digit 4 is wrongly placed in the hint code. Secret code verified.
Clue 5. Code 6 4 2: One digit right correctly placed. (correct code 045)
- Correct digit 4 in its correct position in the middle. Secret code verified.
Secret code [ 0 4 5 ] satisfies all the clues. The missing digit 5 in the rightmost place in the secret code remained happily oblivious of what the clues were discussing — position and correctness of digits — forgetting its existence!
Solution Outline (Concise Version)
Step 1. Exploit the pattern of digit 4 common to four Clues 1 (4 0 8), 3 (0 2 4), 4 (4 9 1) and 5 ( 6 4 2). Apply false assumption logic on 4 in a pair of clues in sub-steps.
- Assume digit 4 wrong → Clue 1 (4 0 8) + Clue 3 (0 2 4) imply three digits 0, 2, 8 to be the three correct digits in the secret code. This violates Clue 4 (4 9 1) as none of (0,2,8) appears in its hint code → Contradiction → Original assumption false and 4 is the right digit.
- From Clue 5, digit 4 is positioned in the middle → Partial secret code: [ ? 4 ? ].
Step 2: Apply positional conflict with the correct digit 4 in Clue 3 to identify the second correct digit.
- In Clue 3 (0 2 4) with one correct digit in correct position and 1 correct digit wrongly placed, digit 2 identified as the incorrect digit by positional conflict in the middle. Elimination of 2 fixes 0 as the second correct digit in leftmost position → Partial secret code [ 0 4 ? ].
Step 3: As the partial secret code satisfies all the clues without revealing the third correct digit, inventive technique of property change analysis is used for finding the elusive third digit.
- With the single focus on identifying a taken-for-granted property of the main actor - the digits in the clues - the possibility of a digit not used at all in the clues came to light → the missing digit 5 is identified as the third correct digit to open the lock → Secret code: [ 0 4 5 ] satisfied all clues.
Lessons Learned
- Common Digits Are Logical Anchors:
- Digit 4 appears in four clues. Recurrence of 4, makes it a prime candidate for combined clue analysis. Always group clues by common digits.
- In Clues 1 and 3, assuming "4 is wrong" led to three correct digits (0,2,8) — none appearing in Clue 4 (hint code: 491). This contradiction proves 4 must be correct — a powerful logical tool. This also confirms its position at the middle from Clue 5 — Partial secret code formed [ ? 4 ? ].
- Analyze Clue 3 (hint code: 024) with correct digit 4 wrongly placed and digit 2 proved to be incorrect by positional conflict in the already occupied middle position. Elimination of wrong digit 2 revealed the second correct digit 0 in its correct leftmost position — Partial secret code formed [ 0 4 ? ].
- In Clue 3, digit 2 suffered a direct positional conflict with digit 4 already occupying middle position providing the second breakthrough.
- The partial secret code satisfying all five clues without revealing the third correct digit in the secret code, a stalemate situation is faced.
- This is the time for out-of-the-box inventive discovery with the help of property change analysis technique.
- Insistent focus on finding a taken-for-granted property of the principal actor, the digits in the clues, revealed that the tenth digit 5 not used in the clues at all — Final solution [ 0 4 5 ].
- Each deduction feeds into the next:
- Step 1. Use Clues 1+3+5 to prove 4 is correct by false assumption logic leading to contradiction → fix its position → 4 takes middle position.
- Step 2. Use Clue 3 to confirm 2 incorrect and eliminated to confirm 0 correct → 0 takes leftmost position.
- Step 3. Realizing that the five clues don't have the third digit, enumerate the digits used in the clues. Identify 5 as the forgotten tenth digit not used in any of the clues to take its rightmost position in the secret code.
- All logic in structured progression.
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