Analyze the one condition and four clues each a 4 digit code with hints on right digit and right place to find the 4 digit code to open the number lock.
The tricky 4 digit number lock riddle 2657
Go through the four clues on four digit codes of a number lock and find the code to unlock the number lock:
- Clue 1: Code 2 6 5 7 : Two digits right but both are at wrong positions.
- Clue 2: Code 0 4 1 5 : One digit right but in the wrong place.
- Clue 3: Code 4 2 6 8 : No digit is right.
- Clue 4: Code 1 7 4 9 : Two digits right and in the right place.
Condition: All 4 digits in the code are different.
Reasoned Steps of Solution of tricky 4 digit number lock puzzle 2657
Use the maximum information bearing clue first
The third clue carries maximum information. Analyze it first.
- The third clue code 4 2 6 8: No digit is right.
- It eliminates the digits 2, 4, 6 and 8. The digits in the clues remaining still as candidates for right digit are only five: 0, 1, 5, 7 and 9.
Next choose the first clue
The first clue: Code 2 6 5 7 : Two digits right but both are at wrong positions.
The four digits in the clue have two of the remaining potentially right candidates 5 and 7 and their places are described. That's why this clue is chosen at the second step.
Objectives:
- To confirm whether these two are the right digits and,
- Get an idea of their right positions in the code.
The clue says: Two digits right but both are at wrong positions.
Conclusion:
- Digits 2 and 6 already identified as wrong, the two right digits must be 5 and 7.
- Possible position of 5 in the code: 1, 2, or 4.
- Possible position of 7 in the code: 1, 2, or 3.
Spot the second clue to analyze in the third step (as its code has already confirmed right digit 5)
The second clue: code 0 4 1 5 : One digit right but in the wrong place.
- Identify 5 as a confirmed right digit. The rest not confirmed as yet. But the clue indicates the code to contain only one right digit.
Conclusions:
- Digit 4 is already identified as wrong. Now 0 and 1 also are identified as wrong. 5 is the only right digit in the clue code.
- Position 4 of digit 5 being wrong in the clue code, possible positions of right digit 5 can only be 1 and 2.
- Right digits: Out of possible right digits 0, 1, 5, 7 ad 9, the digits 0 and 1 are eliminated, the already identified right digits are 5 and 7, and the other possible right digit is only 9 among the digits of the clue codes.
Analyze the last clue and find the code
The fourth clue: Code 1 7 4 9 : Two digits right and in the right place.
Analysis:
- Digits 7 and 9 out of the four are right and their 2nd and 4th positions are right.
Conclusion:
- Out of the possible right positions 1 and 2 of digit 5, 2nd position is now occupied by 7. Right position of digit 5 in the correct code must then be the first.
- The correct code will then be of the form: 5 7 ? 9.
Here is the trick in the puzzle: What will be the digit in the 3rd place of the code? By the given condition of all different digits in the code, the third digit cannot be any of 5, 7 or 9.
Final conclusion:
- The third place right digit must then be 3. This is the only digit left out of ten (though not included in the clue codes cleverly).
The trick is: digit 3 is not mentioned in the clue codes at all. It is kept invisible. But no condition stated the missing digit 3 cannot be a right digit.
The correct code to open the lock is then: 5 7 3 9.
You may try to solve this not so easy puzzle in fewer steps.
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