### Brain Teasers

# Which House?

Mad Ade is telling his friend, Shamus O'Stoatclencher, at which number house he lives at on "Madadia Avenue":

(1) If my house number is a multiple of 3, then it is a number from 50 through 59.

(2) If my house number is not a multiple of 4, then it is a number from 60 through 69.

(3) If my house number is not a multiple of 6, then it is a number from 70 through 79."

What is Mad Ade's house number?

(1) If my house number is a multiple of 3, then it is a number from 50 through 59.

(2) If my house number is not a multiple of 4, then it is a number from 60 through 69.

(3) If my house number is not a multiple of 6, then it is a number from 70 through 79."

What is Mad Ade's house number?

### Answer

Mad Ade's house number is 76.From (1) and (3), the house number must be from 50 to 59 or 70 to 79. Take any number. It will be either a multiple of 3 or not. Also, a number multiple of 6 is always a multiple of 3. Hence, the house number can be 51, 54, 57, 70, 71, 73, 74, 76, 77 or 79.

From (2), if the house number is not a multiple of 4, then it is a number from 60 through 69. There is not a single number between 60 and 69 in short-listed numbers above. Hence, the house number must be a multiple of 4 i.e. 76.

Hence, Mad Ade's house number is 76.

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