Given five clues, each with a 3 digit code and hints on correct digits and placements. Real challenge: Open the number lock using first four clues.

### Real Challenge: Open the 3 digit Number Lock Using First 4 Clues Puzzle

Find the 3 digit code from first four of the five clues to unlock the number lock:

**Clue 1: Code 3 4 2 :** One digit right but wrongly placed.

**Clue 2: Code 2 7 3 :** One digit right but wrongly placed.

**Clue 3: Code 1 6 5 :** Two digits right and are well placed.

**Clue 4: Code 8 5 3 :** Two digits right but in wrong places.

**Clue 5: Code 2 6 4 :** Nothing is correct.

**Recommended time to solve this real challenge: 10 minutes.**

But you may first like to meet the easier **challenge of finding the number lock code using ANY four clues.**

**Recommended time to solve 3 minutes.**

### Solution to the Puzzle Challenge: Open the 3 digit Number Lock Using ANY Four Clues

#### Step 1: Eliminate as many incorrect digits as possible

The Clue 5 is the natural first favorite as it helps to eliminate three digits at one stroke.

**Clue 5: Code 2 6 4 :** Nothing is correct.

**Result:** Digits 2, 4 and 6 are wrong.

#### Step 2: Look for the clue that includes the wrong digits and help to identify correct digits

Clue 1 immediately attracts attention as it includes two of the three incorrect digits.

**Clue 1: Code 3 4 2 :** One digit right but wrongly placed.

**Result:** As digits 2 and 4 are wrong, digit 3 must be the correct one and its correct position must be the second or third.

#### Step 3: Get the correct position of the single correct digit 3

Clue 2 eliminates third (from left) position for 3 and fixes its correct position as the middle.

**Clue 2: Code 2 7 3 :** One digit right but wrongly placed.

**Result:** The correct position of the correct digit 3 is the middle position.

#### Step 4: Deduce the correct code by position exclusion from Clue 3

At this point, the Clue 3 becomes the most important one.

Clue 3: Code 1 6 5 : Two digits right and are well placed.

**Result:** *As middle position has already been booked by correct digit 3, the digit 6 in the middle must be the wrong one and rest two digits 1 and 5 are not only correct, those are also in their correct positions in the code.*

**Solution:** The code to open the lock is **1 3 5.**

This is easy, I suppose. Let's take up the real challenge.

### Solution to the Real Puzzle Challenge: Open the 3 digit Number lock using the FIRST four clues

You would naturally expect this pathway to be more difficult to follow because you have decided to ignore your most potent weapon for the solution: the Clue 5 that declares three digits incorrect at one stroke.

Nevertheless, you have no fear and go forward. Carefully, analytically, Logically.

First goal to crack open a chink in the puzzle is to find at the least one correct or incorrect digit even if you have to analyze more than one clue together.

#### Step 1: First hit: Identify one correct digit from Clue 3 and Clue 4

Consider the two clues:

**Clue 3: Code 1 6 5 :** Two digits right and are well placed.

**Clue 4: Code 8 5 3 :** Two digits right but in wrong places.

Your immediate attention shifts to the digit 5 appearing in both. With a bit of convoluted logic, you reason:

If digit 5 is the incorrect digit, there would be as many as FOUR correct digits 1,3,6 and 8 which is not possible for a 3 digit code. So, the only possibility is: digit 5 must be one of the two correct digits and its correct place is: third from left.

In spite of this breakthrough, next step is not very clear and needs careful analysis.

#### Step 2: Identify the second correct digit from the first and second pairs of clues

What the first two clues tell us?

**Clue 1: Code 3 4 2 :** One digit right but wrongly placed.

**Clue 2: Code 2 7 3 :** One digit right but wrongly placed.

**Result:** One of the four digits 2, 3, 4 and 7 is the correct digit. Nothing much.

Reconsider the second pair of clues:

**Clue 3: Code 1 6 5 :** Two digits right and are well placed.

**Clue 4: Code 8 5 3 :** Two digits right but in wrong places.

**Result:** One of the four digits 1, 3, 6 and 8 is a correct digit.

Again take hep of negative reasoning and assume digit 3 common to three of the four clues as incorrect.

This implies:

- From Clue 4,
*digit 8 must be the second correct digit occupying the middle place.* - In Clue 3, due to positional conflict with digit 8, digit 6 is eliminated.
- And
*digit 1 must be the third correct digit.*

**In Clues 1 and 2, none of these two apparently correct digits, 1 and 8 appear.** *As digit 3 is assumed as incorrect, Clues 1 and 2 won't have any single correct digit.*

**This violates the original assumption of digit 3 as incorrect.** So,

**Certain result:** Digit 3 must be the single correct digit in Clues 1 and 2 and its position is the middle one.

#### Solution to the Real Challenge

From Clue 3, digit 1 must be the third correct digit occupying the first position from left.

**The code to open the lock is 1 3 5.**

Verify the correctness of the code against all the five clues.

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