Solve 3 digit number lock puzzle 403 in minimum steps from 5 clues, each containing a 3 digit code with digit and position correctness description.
3 Digit Number Lock Puzzle With Hint Code 403
Following are the five clues:
Clue 1: Code 4 0 3: Two digits are correct and in the right places.
Clue 2: Code 3 0 4: Two digits are correct — 1 in the right place and 1 in the wrong place.
Clue 3: Code 3 5 0: Two digits are correct but both are in the wrong places.
Clue 4: Code 3 1 2: Two digits are correct but both are in the wrong places.
Clue 5: Code 0 1 6: Two digits are correct but both are in the wrong places.
Find the 3 digit code to open the number lock in minimum number of analytical steps.
Time to solve: 15 minutes.
Challenge met: Solved 3 Digit Number Lock Puzzle 295 in Minimum Steps
Digit 3 appears in four clues. This is the key pattern to be used.
Step 1. False assumption logic, positional conflict and incorrect digit elimination produce two correct digits
Apply false assumption logic on most frequently occurring digit 3 in combined analysis of all four clues in which it appears.
Clue 1: Code 4 0 3: Two digits are correct and in the right places.
Clue 2: Code 3 0 4: Two digits are correct — 1 in the right place and 1 in the wrong place.
Clue 3: Code 3 5 0: Two digits are correct but both are in the wrong places.
Clue 4: Code 3 1 2: Two digits are correct but both are in the wrong places.
- False assumption logic on Clues 1+2+3+4: Assume 3 wrong ➡ In four clues digits (0,1,2,4,5) correct ➡ impossibility ➡ assumption wrong, digit 3 right in rightmost position from Clue 1 ➡ partial secret code [ ? ? 3 ].
- Clue 2: 3 correct in wrong position ➡ in the hint code if 4 is correct, it is in positional conflict with rightmost 3 in secret code ➡ 4 incorrect and 0 correct in middle ➡ partial secret code [ ? 0 3 ].
Step 2. Third digit by digit and placement patterns in combined clues
Need to choose the right digit to occupy the leftmost position between 1, 2 and 6 from Clues 4 and 5.
Combined digit-position pattern analysis of Clues 4 and 5 promises breakthrough.
Clue 4: Code 3 1 2: Two digits are correct but both are in the wrong places.
Clue 5: Code 0 1 6: Two digits are correct but both are in the wrong places.
- 2 correct produces secret code 203 ➡ Violates Clue 5 ➡ 2 incorrect.
- 6 correct produces secret code 603 ➡ Violates Clue 4 ➡ 6 incorrect.
- In Clue 5, digit 0 correct and wrongly placed ➡ with 6 incorrect, 1 is the third correct digit.
- Solution: Lock opening code: [ 1 0 3 ].
Verification of the solution
Check all clues against correct code 103:
- Clue 1 (4 0 3): Two digits are correct and in the right places: 0 and 3 are the correct code digits in right places — matches
- Clue 2 (3 0 4): Two digits are correct — 1 in the right place and 1 in the wrong place: 0 and 3 are the correct code digits, 0 in right place, 3 wrongly placed — matches.
- Clue 3 (3 5 0): Two digits are correct but both are in the wrong places: 0 and 3 correct code digits, both wrongly placed — matches.
- Clue 4 (3 1 2): Two digits are correct but both are in the wrong places: 1 and 3 correct code digits, both wrongly placed — matches.
- Clue 5 (0 1 6): Two digits are correct but both are in the wrong places: 0 and 1 correct code digits, both wrongly placed — matches.
Answer: 103.
Lessons learned
1. Detection of key patterns identifies four positive clues (stating hint code digit correctness) and one digit common to all — combined clue analysis promises multiple breakthroughs.
- Clues 1, 2, 3 and 4 are analyzed first.
2. False assumption logic — Use of key patterns: Assume the common digit wrong. In case of a contradiction, the false assumption is proved wrong, and the wrong digit right. Otherwise, no contradiction (in rare cases) implies (does not ascertain) validity of the assumption in the clues analyzed. Verification from remaining clues would then create the breakthrough.
- Common digit 3 assumed wrong led to five correct digits (0,1,2,4,5) — an impossibility. The contradiction confirmed 3 correct in rightmost.
3. Importance of forming the partial code:
- Partial code [? ? 3 ] meant: Two places vacant with rightmost blocked. Helps position conflict breakthrough in later clue analyses.
4. Position conflict: In one or more clue analysis, digit patterns create a conflict between an aspiring correct digit and an already identified correct digit confirming the contender wrong.
- In Clue 2 (3 0 4), with correct code digit 3 wrongly placed, if 4 were to be correct, it cannot occupy rightmost (already blocked by correct code digit 3) and confirmed wrong. This creates the second breakthrough correct digit 0 in middle ➡ partial secret code: [ ? 0 3 ].
5. Combined Digit-Position Correctness analysis: Digit and position correctness patterns in multiple clues promise breakthrough.
- Clues 4 (3 1 2) + 5 (0 1 6): Assuming either 2 or 6 correct creates violation in digit correctness descriptions of Clue 5 and Clue 4 respectively (both clues needed two correct digits) — 2 and 6 proved incorrect. It led confirmation of remaining digit 1 as the third correct digit.
- Solution [ 1 0 3 ].
6. All analysis of successive pattern based right clue choices, using the patterns for position and digit correctness analysis and successive breakthroughs in steps.
Solution reached in two steps, the minimum.
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