# Mastermind

You must find a 3-digit number. You know that:

• 682 shares one digit with the number, and it is well placed;
• 614 shares one digit with the number, but it is wrongly placed;
• 296 shares two digits with the number, but they are wrongly placed.

What is the number?

The first and second clues imply that the 6 is not a part of the number. The third clue then implies that 2 and 9 are parts of the number. Now the first clue implies that 2 is the last digit of the number, and the third clue implies that 9 is the first digit of the number. Finally, the second clue implies that 4 is the second digit of the number. Therefore, the number is 942.

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#### Responses

1. Can you please explain how come clue 1 and 2 implies 6 is not part of the three digit number?

1. Of course KK. The only digit which the numbers 682 and 614 have in common is 6. However, if 6 is indeed in the three digit number, then the first clue states that it must be in position 1, whereas the second clue states that it must not be in position 1. This is a contradiction and therefore 6 is not a part of the number.

1. Dude 1st clue doesn’t say about 6 ..Think about 2 u will get the answer and right answer is 962..those who understand First clue get the answer

1. Hello Padder. 962 shares two digits with 682, which contradicts with the 1st clue.
If 6 was part of the number, then from the 1st clue it follows that the 6 must be the first digit. However, this contradicts with the 2nd clue, which says that no digit in 614 is in the correct place.