Can you find the code to open the 3 digit number lock from the five clues each with a code and placement description? Go for the most efficient solution.
3 Digit Number lock puzzle with five clues including 682
Following are five clues each with a three-digit code for a number lock. Find the code to open the lock from the clues.
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 clues, find the three-digit code that will open the number lock. Try to use the minimum number of Clues for the most efficient solution.
Time to solve: 10 minutes.
Solution to the 3 digit number lock puzzle with five clues including 682
A. Identify the correct or the wrong digits
STRATEGIC STEP 1: Choose Clues with Position and Correctness Conflict:
Identify the promising pair of clues 1 and 2. In both, digit 6 appears in 1st position with conflicting placement and correctness descriptions.
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.
- If digit 6 is the right digit by Clue 1, its right position is the first, but by the second Clue, the right digit in the first place is wrongly placed. The conflict identifies the digit 6 as wrong.
For no other digit in the two Clues, you can reach such a certain conclusion.
STRATEGIC STEP 2: Take up the Clue that mentions the wrong digit - Link reference technique:
Look for a clue with digit 6, the already identified incorrect digit. It will help in identifying right digits. Such a Clue is Clue 3.
Clue 3: Code 206: Two digits are right, but both are in the wrong place.
- As digit 6 is wrong, both digits 2 and 0 are the two right digits, but in wrong places.
B. Find the correct placements of the two right digits
LINK REFERENCE: Return to Clue 1 with single right digit 2.
Clue 1: Code 682: One digit is right and is in its place.
- Digit 2 already identified as a correct digit. Position of digit 2 in the correct code is the rightmost.
Analyze Clue 3 again as it includes both correct digits 2 and 0 (Link reference).
Clue 3: Code 206: Two digits are right, but both are in the wrong place.
- In the lock opening code, Digit 2 occupies the rightmost position, and middle position for the other right digit 0 is wrong by Clue 3. So, right position for digit 0 must be the leftmost in the lock opening code.
- The code to open the lock is of the form 0 ? 2.
C. Identify the third right digit for solution of the number lock riddle
Choose Clues Suitable for Positional Constraint Analysis:
Observe in Clue 2, one of the two possible right digits 1 and 4 (as digit 6 is wrong) occupies the only available middle position in the lock opening code.
Clue 2: Code 614: One digit is right and is in the wrong place.
- Digit 1 occupies the only available middle position, and its position is wrong. Digit 1 doesn't have any place in the correct code.
- Digit 1 is the second wrong digit in 614.
- Digit 4 is the 3rd right digit and its position is in the middle of the lock opening code.
The code to open the number lock is 0 4 2.
The Clue 4 and Clue 5 remain unused in this solution. This confirms it as the most efficient solution.
Truth is: No knowledge is ultimate. You must verify every bit of concepts you gather with your own mental abilities and then accept, disprove or extend it.
Don't ignore the unused Clues. Use these two to verify your solution and know for certain that it is bulletproof with no chinks.
End note
Strategic techniques used
- Position and correctness conflict: In two Clues, a digit occupies the same position with different correctness descriptions - one correct and the other wrong.
- Link reference technique: Analyzing Clues that mention an already identified correct or wrong digit.
- Positional constraint analysis: Analyzing Clues in which a number of digits may occupy one correct position, but by the Clue, one of these is in the wrong place. This digit must be the wrong one.
Use of strategic techniques and analysis of one or more Clues together in the right sequence ensured the most efficient solution.
A Small Challenge for You
Why don't you start with Clue 4 that identifies THREE digits as wrong at one go! That conventional path might lead you to a more efficient solution! Who knows!
To enjoy solving many more such number lock puzzles, click here.
Puzzles you may enjoy
Easy to hard brain teasers with systematic solutions
Challenging brain teasers with solutions: Long list.
This will always be the most up-to-date full list with the brain teasers classified into categories that can be browsed separately.