Question

Crack the code,a numeric lock has 3 digit key,682 one number is correct and well placed,416 one number is correct but wrongly placed,206 two numbers are correct but wrongly placed,738 nothing is correct,780 one number is correct but wrongly placed

Answer 1

Given:

A numeric lock has 3 digit key,

682 one number is correct and well placed,

416 one number is correct but wrongly placed,

206 two numbers are correct but wrongly placed,

738 nothing is correct,

780 one number is correct but wrongly placed

To find:

Crack the code

Solution:

Clues 1 & 2

- number 6 is not included as it cannot be in both the wrong and the right place at the same time

Clue 3

- 2 and 0 are included

Clue 1

- 2 must be in the last position

Clue 3

- 0 must be in the first position

Clue 2

- 1 & 4 as possible values, but only 4 is not in the middle position

042 is the code.

Answer 2

Therefore, the co-de of the given numerical lock is 042.

Decoding the clues given:

On observing the rules given, from the fourth rule, we get that the lock contains no numbers from the list [7, 3, 8]. So, from the first rule 6, 2 remains.

From the second rule, we get that one number among 6, 1, 4 is correct but wrongly placed. But the number 6 is in the same position in rules 1 and 2. So, there is no chance of 6 being among the three numbers of the lock.

So, from the first rule, we get that the number at the last position is 2 as it says that the number is well placed.

_ _ 2

In the third rule, if we eliminate 6, the remaining numbers are 2, 0. They are correct but wrongly placed. As 2 is fixed with the last position, 0 goes for the first position as per the rule.

0 _ 2

Now, from rule 2, we get that one number is correct among 1, 4 but is wrongly placed. If 1 is correct, it would be well placed and that contradicts the rule which says that the number is wrongly placed. So, the correct number that should be in the second position is 4

0 4 2

Therefore, the co-de of the given numerical lock is 042.

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