I'm thinking of a number.

• if it is not a multiple of 4, then it is between 60 and 69
• if it is a multiple of 3 it is between 50 and 59
• if it is not a multiple of 6 it is between 70 and 79.

What is the number?

The number is 76.

If the number is not a multiple of 4, it must be between 60 and 69 (first condition). It, then, can neither be a multiple of 3 (second condition) and must be a multiple of 6 (third condition). Yet, as numbers that are multiple of 6 are also multiples of 3, this would lead to a contradiction, thus the number IS a multiple of 4, and, thus, can not be between 60 and 69.

None of the numbers between 50 and 59 are both multiples of 3 and 4 (i.e., a multiples of (3 x 4) = 12: 12, 24, 36, 48, 60, ...); therefore the number can not be be a multiple of 3 and can not be between 50 and 59.

The number being a multiple of 4 and not a multiple of 3, can not be a multiple of 6. Thus, the number must be between 70 and 79. In this range, only 72 and 76 are multiples of 4; yet, 72 is a multiple of 3, leaving only 76. Therefore, the number to guess is 76.

Posted by Dej Mar on 2008-08-19 12:11:32