Can you determine the professor's house number ?

Question

A maths professor asked one of his students to visit his house regarding some work.
The student asked the professor his house number.
The professor replied in a strange way :

1. If my house number is a multiple of 3, then it is a number from 50 to 59.
2. If my house number is not a multiple of 4, then it is a number from 60 to 69.
3. If my house number is not a multiple of 6, then it is a numbre from 70 to 79.

Can you determine the professor's house number ?

Answer 1

1. Multiple of 3, then it is a number from 50 to 59 = 51, 54, 57
2. Not a multiple of 4, then it is a number from 60 to 69
   = 61, 62, 63, 65, 66, 67
3. Number is not a multiple of 6, then it is a number from 70 to 79
   = 70, 71, 73, 74, 75, 76, 77, 79.

Now the Professor's house number can either be a multiple of 3 or not ie., 51, 54 & 57 are possibilities. But none of them are a multiple of either 4 or 6.
For the 2nd case possibilities are
61, 62, 63, 65, 66, 67 out of which 63, 66 are multiples of 3
and the rest are not a multiple of 6 and hence cant be the door number either

For the 3rd case the possibilities are
70, 71, 73, 74, 75, 76, 77, 79. Out of which 75 is a multiple of 3 and the rest except 76 are not multiples of 4.
That leaves 76 as the only possible answer for the Professor's house number.

Answer 2

76

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Rule #1: divisible by 3: then in 50 - 59
Rule #2: not divisible by 4: then in 60 - 69
Rule #3: not divisible by 6: then in 70 - 79

h = house number

50-59
rule 1: h must be 51, 54, 57
rule 2: h must be 52, 56
rule 3: h must be 54
common: none

60-69
rule 1: h must be 61, 62, 64, 65, 67, 68
rule 2: h must be 61, 62, 63, 65, 66, 67, 69
rule 3: h must be 60, 66
common: none

70-79
rule 1: h must be 70, 71, 73, 74, 76, 77, 79
rule 2: h must be 72, 76
rule 3: h must be 70, 71, 73, 74, 75, 76, 77, 79
common: 76

house number is 76