Can you find the three-digit code to open the number lock? You have five clues each based on a code combination. Time to solve the riddle, 10 minutes.
Open the lock riddle with clues including 682
Following shows five clues each based on a three-digit code for a number lock. From the clues, find the code that will open the lock.
Clue 1: Code 682: One digit is right and is in its place.
Clue 2: Code 614: One digit is right and is in the wrong place.
Clue 3: Code 206: Two digits are right, but both are in the wrong place.
Clue 4: Code 738: All digits are wrong.
Clue 5: Code 380: One digit right and is in the wrong place.
From the five clues, find the three-digit code that will open the number lock.
Time to solve: 10 minutes.
Solution to Open the lock riddle with clues including 682
Clue 1 by itself cannot help in making any conclusion, but from clue 2 combined with clue 1, get the first result,
Conclusion 1: Digit 6 is not the right digit in 682, and,
Either 8 or 2 is the right digit in the right place in 682.
Skip 3rd clue on code 206 and move on to the 4th clue on 738. Discover, among the three, digit 8 is also wrong.
Together with the first result conclude,
Conclusion 2: Digit 2 is the right digit and is in the right place in 682.
Back to the 3rd clue on 206 with two right digits, you know already—2 is a right digit and 6 is a wrong digit. So,
Conclusion 3: The third digit 0 must be a right digit and it must be in leftmost place of the three-digit code.
The code is in the form “0 ? 2”.
Analyze the last clue to identify both 3 and 8 are wrong and 0 is right, but in the wrong place. This doesn’t give any clue on the missing middle digit.
When you look back,
You find 2nd clue still has untapped information with rest of the clues exhausted of their potential.
Already known in clue 2 on 614: Digit 6 is wrong.
Conclusion 4: So digit 1 or 4 is the right digit.
Recall now that only the middle position in the code is still to be filled.
Final reasoning: As digit 1 holds this second middle position in 614 and the clue says, “the right digit is in the wrong place”, digit 1 must be wrong.
Finally,
Conclusion 5: Digit 4 turns out to be the right digit in the wrong place in 614 and the code is 042.
Comment
This is a reasoning puzzle with each clue a condition to be processed together with other clues gradually moving towards the solution. Challenge is how quick you can reach the solution.
There are many possible code-clue combinations in this class of riddles. We’ll cover another variation of this code-clue combination that starts with 682.
Variation in Open the lock riddle with clues including 682
Following shows five clues each based on a three-digit code for a number lock. From the clues, find the code that will open the lock.
Clue 1: Code 682: One digit is right and is in its place.
Clue 2: Code 645: One digit is right and is in the wrong place.
Clue 3: Code 206: Two digits are right, but both are in the wrong place.
Clue 4: Code 738: All digits are wrong.
Clue 5: Code 780: One digit right and is in the wrong place.
From these five clues, find the three-digit code that will open the number lock.
Time to solve: 10 minutes.
Solution to the Variation in Open the lock riddle with clues including 682
As before, from clues 1, 2 and 4, first conclude,
Conclusion 1: Digits 6 and 8 are wrong, digit 2 is right and is in correct place.
So the code is in the form “? ? 2”. First two digits from left to be identified.
Clue 1 exhausted of its potential but not clues 2 and 4.
From clues 4 and 5, conclude,
Conclusion 2: Both digits 7 and 8 are wrong and digit 0 is right, but is in the wrong place. The 3rd position from left already occupied by digit 2.
The second right digit 0 will occupy either first or the second place from left.
Clue 5 exhausted of its potential.
Time to take up clue 3: In 206 two digits are right and both are in the wrong place.
You know digit 2 and 0 are the two right digits, and second position from left is wrong for digit 0.
Conclusion 3: Digit 0 must occupy the first position from left.
The code at this point is in the form, “0 ? 2”. The 3rd right digit left to identify can take only the middle position.
Examine the clues. Potential of clue 3 exhausted, but clue 2 still has useful information left in it.
Analyze Clue 2: Code 645: One digit is right and is in the wrong place.
You already know digit 6 is wrong. So either digit 4 or digit 5 is right.
Reasoning: Digit 4 occupies the middle position, the only position left for the 3rd digit in the code. So if 4 were the right digit its position would also have been right. But the clue says that the position of the right digit is wrong in 645.
Conclusion 4: Digit 4 cannot be the right digit and digit 5 must be the right digit. Its position in 645 is wrong as it will take the middle position in the code.
It confirms,
The code in this case is 052.
In both cases, the last conclusion is a little tricky.
End note
The key to quick solution of reasoning puzzles is processing the most suitable clue or condition either individually or together with other clues.
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