Can you crack the number lock puzzle 241 in one big step? The five clues have hint codes and hints on digit and placement correctness.
The 3 Digit Number Lock Puzzle 241 5 Clues
Following are the five clues each with a 3 digit hint code for a number lock and descriptions of the correctness of digits and positions.
Clue 1: Code 2 4 1 : One digit right and in right position.
Clue 2: Code 4 1 3 : All digits are wrongly placed.
Clue 3: Code 5 3 2 : Two digits right but wrongly placed.
Clue 4: Code 3 4 7 : One digit right but wrongly placed.
Clue 5: Code 7 5 1 : Two digits right but wrongly placed.
Find the 3 digit code that will open the number lock in one big step.
Time to crack the code: 15 minutes.
Hint: Analyze all the clues with breakthrough patterns of digits common to the clues.
Solution to Crack the Number Lock Puzzle 241 in One Big Step
A brief scan through the clues revealed a strange clue in Clue 2: Code 413. It says, all digits are wrongly placed. It may mean,
- All are correct digits, but all are wrong position in the hint code.
- All digits in 413 that are correct are in wrong places, or even,
- All digits are wrong and so these are obviously stated to be wrongly placed - these in fact, are located outside the secret code.
Being unsure of the exact meaning of the clue, let us keep our mind open and depend more on discovering first all incorrect digits possible, and with their help, the correct digits.
We will depend on our ability to identify common digit patterns in a collection of clues to draw certain conclusions of incorrectness first (that is always easier than finding a correct digit at first).
Step 1. Discovering the first incorrect digits by position and correctness conflict
This is the most commonly used technique in identifying an incorrect digit based on the pattern:
Position and correctness conflict: A digit common to two clues appear in the same position, both clues says, one or two digits in the hint code right, but in one hint code in right place and in the other wrongly placed. This conflict of a probable right digit produces a contradiction of the digit being right in the same position in the hint codes, but stated as in right place in one clue and wrong in the other. This contradiction proves the digit to be incorrect and beyond the contradiction (out of the clue).
Take up Clues 1, 4, and 5 to identify two such incorrect digits in one compound step (consisting of more than one elementary steps):
Clue 1: Code 2 4 1 : One digit right and in right position.
Clue 4: Code 3 4 7 : One digit right but wrongly placed.
Clue 5: Code 7 5 1 : Two digits right but wrongly placed.
- In Clues 1 and 5, digit 1 appears in both rightmost, but with conflicting position descriptions. If 1 is right, it cannot be in the same position in one hint code and stated as rightly placed and in the other as wrongly placed
- 1 is an incorrect digit.
- Same way, 4 in Clues 1 and 4 is identified as the second incorrect digit.
- In Clue 1, both 1 and 4 identified as wrong, 2 must be right and is in its position in the secret code.
- In clues 4 and 5, 1 being wrong, both 5 and 7 are right. 7 can take middle or right places, but 5 can take only the right. That leaves the middle place for 7.
- The lock opening code is [ 2 7 5 ].
Puzzle solved in one single compound step consisting of a chain of reasoning based on largely common digit patterns in clues and corresponding position descriptions.
Verify the solution from the remaining two unused clues.
Clue 2: Code 4 1 3 : All digits are wrongly placed.
- None of the three digits are in the secret code. Technically the digits are wrongly placed, outside the code. Secret code 275 verified.
Clue 3: Code 5 3 2 : Two digits right but wrongly placed.
- 2 and 5 are in the code 275, but in different places. The description of the two correct digits being wrongly placed are indeed correct. Secret code 275 agrees with the Clue 3.
Lessons learned
- First step should always be to scan or examine all the clues together to spot an usual clue, promising clues and decide the strategy of analysis of the clues.
- As a result of the scan, Clue 2 proved itself to be quite ambiguous, but it was ignored strategically.
- Position and correctness conflict between two common digits in two pairs of Clues 1 and 5, and 1 and 4, identified digits 1 and 4 as incorrect.
- Incorrect digit elimination of 1 and 4 in Clue 1 gave us a correct digit 2 along with its correct position as leftmost.
- Same way, elimination of incorrect digit 1 in Clue 5 gave us, two correct digits 7 and 5.
- Digit position analysis on 7 and 5 in Clue 5 along with the additional information of correct digit 2 already taking up the leftmost position determined the correct position of both 5 and 7.
All done one long chain of digit and position pattern based analysis in one big compound step.
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