Crack number lock puzzle 578 in one step from 5 clues, each with a 3 digit code and statement on digit and position correctness on the hint code.
3 Digit Number Lock Puzzle Including Hint Code 578
Following are the five clues:
Clue 1: Code 5 7 8: Two digits are correct and in the right places.
Clue 2: Code 7 2 3: One digit is correct but in the wrong place.
Clue 3: Code 4 9 1: No digit is correct.
Clue 4: Code 6 7 3: One digit is correct but in the wrong place.
Clue 5: Code 5 6 0: One digit is correct and in the right place.
Find the code to open the number lock in one step of reasoning chain.
Time to solve 10 minutes.
Hints: Go through the clues carefully. Search for the key pattern ad other supporting patterns in the clues. You'll find these breakthrough patterns hidden in common digits across multiple clues. More the number of clues you analyze together, faster will be the solution.
Solution to Crack Number Lock Puzzle 578 in a Single Step
All three wrong digits in Clue 3 (the wrong digits clue) not appearing in other clues, it cannot be used in solution. The puzzle effectively is a four-clue number lock puzzle.
The key pattern of digit 7 common in three positive clues (with positive digit correctness) should provide you a quick breakthrough.
Step 1. False assumption turns right to gift you the solution in one step — Power of False Assumption Logic
In positive Clues 1, 2 and 4, digit 7 is common—points to the most promising path.
Clue 1: Code 5 7 8: Two digits are correct and in the right places.
Clue 2: Code 7 2 3: One digit is correct but in the wrong place.
Clue 4: Code 6 7 3: One digit is correct but in the wrong place.
- Clues 1+2+4: False assumption: Assume 7 wrong ➡ from Clue 1, implied partial secret code [5 ? 8].
- ➡ Clue 2: Digit 2 locked out and incorrect ➡ 3 correct in middle ➡ implied secret code [ 5 3 8 ] — based on assumption, conclusions are uncertain.
- ➡ Verify Secret Code [ 5 3 8 ] against all clues and it successfully satisfies all.
- ➡ Original assumption proves correct.
- Final solution: secret code [ 5 3 8 ].
Solution in one step.
Lessons Learned
1. Combined Clue Pair Analysis with One Digit Common: More clues you analyze in combination, more the breakthrough promise.
- Clues 1+2+4 with digit 7 common with a mix of digit placement correctness, a digit pattern identified that is most promising.
- Common digit pattern in multiple clues provides most breakthroughs in number lock puzzles.
2. False assumption logic: Common digit assumed wrong, an assumption based on the digit wrong property.
- Frequently, the assumption leads to a contradiction and proves the wrong digit correct.
- But, it also is possible for the assumption leads to no contradiction in the clues analyzed. Analysis continues with the assumption and produces major breakthroughs implied and uncertain.
- In analyzing Clues 1+2+4, assuming "7 is wrong" led to no contradiction and produces an implied, still uncertain secret code in one analytical step.
3. Verification against all clues proves the false assumption to be right with certainty:
- As all-clue verification takes little time, proceeding with implied conclusions is the most pragmatic approach.
- If the implied conclusions produce a contradiction, the original false assumption is proved wrong and produces critical breakthroughs (though, when an implied result satisfies three of five clues, chances are: the implied results will be correct).
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