Puzzle of the Day: 85
House Number
My house has a 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 my house number?
My 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, My house number is 76.
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