Can you find shortest solution to number lock puzzle including 082? Its 5 clues each provides a hint code and digit and position correctness description.
The Number Lock Puzzle Including 082 in its Clues
Clue 1: Code 6 4 7: Two digits are correct but both are in the wrong places.
Clue 2: Code 0 8 2: No digit is correct.
Clue 3: Code 2 7 5: Two digits are correct but both are in the wrong places.
Clue 4: Code 3 8 5: One digit is correct but in the wrong place.
Clue 5: Code 9 8 6: One digit is correct and in the right place.
Find the shortest, minimum step solution to the puzzle using the clues.
Time to solve: 5 minutes.
Hint: For the quickest solution, use the most powerful resource in the clues.
How to Find the Shortest Solution to Number Lock Puzzle Including 082
Strategic decision: A brief scan through the clues reveal the most promising clues that produces together two correct digits and their positions in one step.
Step 1. Identify two correct digits at one go and find their correct places
Clue 1: Code 6 4 7: Two digits are correct but both are in the wrong places.
Clue 2: Code 0 8 2: No digit is correct.
Clue 3: Code 2 7 5: Two digits are correct but both are in the wrong places.
- With 2 incorrect from Clue 2, digits 5 and 7 are identified as two correct digits but in wrong places from Clue 3.
- Clues 1 and 3 identify both the rightmost and middle positions wrong for the correct digit 7. Digits 7 has its correct place in the leftmost position.
- With leftmost position blocked and rightmost position wrongfor the second correct digit 5, it must occupy the middle position in the lock opening code.
- Partially formed lock opening code: [ 7 5 ? ].
Step 2. Discover the third correct digit to crack the code in two steps
The positive Clue 5 (with both position and digit correctness "right") with 9 and 8 in leftmost and middle positions provides the breakthrough.
Clue 5: Code 9 8 6: One digit is correct and in the right place.
- Digits 9 and 8 occupy already blocked positions leftmost and middle and must be incorrect.
- Digit 6 is the only correct digit in the Clue in its right position in the code.
- Lock opening code is [ 7 5 6 ].
This is the shortest solution in two steps for opening the number lock.
Verify the code against the unused Clue 4.
Clue 4: Code 3 8 5: One digit is correct but in the wrong place.
- The clue has the only correct digit 5 which indeed is in a wrong place in the code. Code and clue verified.
An exercise for your brain
Is it possible to crack the code without using Clue 2?
If you do take up the challenge, it sure will enhance your ability to explore all possible paths to the solution of a problem - a valuable gain.
Lessons from the solution
- Strategy of analyzing multiple clues together:
- This no-fail strategy usually provides amazing breakthrough results.
- Analyzing Clues 1, 2 and 3 revealed two correct digits and their correct places in one step.
- Strategy of using the maximum information resource in "Nothing correct" Clue 2:
- Getting the incorrect digit 2 from the maximum information "Nothing correct" Clue 2 enabled identifying correct digits 5 and 7 in Clue 3.
- Positional block pattern:
- Blocks in the rightmost and the middle positions for correct digit 7 from Clues 1 and 3 fixed its position as the leftmost.
- This in turn blocked one of the two positions available to the second correct digit 5 in Clue 3 and fixed its position in the middle.
- Positional conflict:
- In positive Clue 5, digits 9 and 8 suffered positional conflict with correct digits 7 and 5 occupying the two positions in the partially formed code. This identified both as wrong.
- Incorrect digit elimination:
- Though this pattern seems to be obvious, it played the final role in identifying the third correct digit 6 in Clue 5 when the the other were eliminated as incorrect.
Identification of common digit patterns in multiple clues and using the patterns effectively enabled the shortest solution.
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.