Can you find the 3 digit number lock code from five Clues each based on a code and a placement description? Solve using least number of Clues in 10 minutes.
3 digit Number Lock Puzzle with Five Clues Including 154
As hints, following are the five Clues each with a code and a placement description. Use the hints in the Clues to find the code for opening the lock.
Clue 1: Code 154: One digit is right and is in the correct place.
Clue 2: Code 431: One digit is right, but in the wrong place.
Clue 3: Code 813: Two digits are right and both are in correct place.
Clue 4: Code 268: One digit is right, but in the wrong place.
Clue 5: Code 435: Two digits are right, but both are in the wrong place.
From the Clues, find the 3 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 Clues Including 154
Step A. Identify a correct or a wrong digit
STRATEGY 1: Choose Clues with Position and Correctness Conflict:
First objective in solving a number lock riddle is to eliminate incorrect digits or find correct digits. Usually, no clue alone can do either (and even if there is such a Clue, ignore it and choose multiple Clues).
- More than one Clue are to be analyzed together.
- In the Clues, one digit should appear in both with conflicting position and correctness descriptions (such as both FALSE).
- Logic analysis will reveal the correct or the wrong one.
Following this idea, use Clue 1 and Clue 3 together (digit 1 common to both) to get the first breakthrough.
Clue 1: Code 154: One digit is right and is in the correct place.
Clue 3: Code 813: Two digits are right and both are in correct place.
- Logic Analysis: In the first Clue on 154, if 1 is the right digit, its correct code place is the leftmost. But, by the 3rd clue on 813, correct code place for digit 1 is the middle position if the digit is right. The two Clues have conflicting correctness and position descriptions for digit 1 and both cannot be true.
The only possibility is,
- Conclusion 1: Digit 1 is a wrong digit.
For no other digit in the two Clues, you can reach such a certain conclusion.
STRATEGY 2: Choose the Clue that mentions the wrong digit - Link reference technique:
Now look for a Clue with the incorrect digit 1. In Clue 3, digit 1 appears, and it helps to mark two correct digits at one go.
Clue 3: Code 813: Two digits are right and both are in correct place.
- Conclusion 2: As digit 1 is wrong, digits 8 and 3 are the two right digits and are in the correct places. The correct code is like “8 ? 3”. Only the middle digit to discover now.
The third Clue has exhausted its potential.
Step B. Identify the third correct digit and solve the number lock puzzle most efficiently
STRATEGY 3: Positional constraint analysis: Analyze for positional conflicts on the only free middle position:
Consider the clinching Clue 1:
Clue 1: Code 154: One digit is right and is in the correct place.
- In Clue 1, the digits 1 and 4 in the leftmost and rightmost positions cannot be the right digits as these are already occupied by correct digits 8 and 3 respectively in the lock opening code. Both digit 1 and digit 4 are incorrect because of positional conflicts.
- Final conclusion: Digit 5 is occupying the only available middle position and by the Clue description, it must be the single correct digit in the code correctly placed.
The code to open the number lock is 8 5 3.
The 2nd, 4th and 5th Clues remain unused. This is a measure of efficiency of the solution. The number lock riddle is solved using only two Clues. Isn't it amazing! But, hold on. Use the free resources of the three unused Clues to verify the correctness of your solution—an application of the Free Resource Use Inventive Principle.
There can't be any doubt that, this is the most efficient solution of this 3 digit number lock puzzle with five Clues including 154.
End note
Strategic techniques used
- Position and correctness conflict: In two Clues, one digit occupies two different positions with conflicting position and correctness descriptions. This conflict identifies the digit as a wrong one.
- Link reference technique: Analyzing a Clue that mentions an already identified incorrect digit, helping to discover correct digits.
- Positional constraint analysis: With the lock opening code having only one position free to occupy, the clinching Clue with one correct digit correctly placed identifies the correct digit in the free place, the rest two eliminated by positional conflicts.
Use of strategic techniques and analysis of one or more Clues together in the right sequence ensured the most efficient solution.
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