[bonanova]

To the nearest whole number, add the number of times the moon rotates about its axis during a lunar month and the number of times the earth rotates about its axis during a calendar year. Other than unity and the number itself, how many factors does this sum have?

[Prof. Templeton]

Zero

Spoiler for because:

366.25 + 1 = 367

Which is a prime number

[Guest]

Zero

Spoiler for because:

366.25 + 1 = 367

Which is a prime number

Doesn't the earth only rotate about its axis 365.25 times a year? So

Spoiler for The answer:

Would be 366, which has 6 factors, 2, 183, 3, 122, 6, and 61.

[Prof. Templeton]

Doesn't the earth only rotate about its axis 365.25 times a year? So

Spoiler for The answer:

Would be 366, which has 6 factors, 2, 183, 3, 122, 6, and 61.

There in lies the trick to this question.

Rotates 365-1/4 times in a year, but you add one rotation for the trip around the sun.

[Guest]

There in lies the trick to this question.

Rotates 365-1/4 times in a year, but you add one rotation for the trip around the sun.

I see! Wow, very tricky indeed.

[Guest]

I see! Wow, very tricky indeed.

"the number of times the earth rotates about its axis"

doesn't include the revolution about the sun, right?

[Guest]

"the number of times the earth rotates about its axis"

doesn't include the revolution about the sun, right?

It actually does, even though it is counter intuitive. For example, if earth was phase locked with the sun, and it was always day for half the world always, we would still make 1 complete revolution each year. And actually now that I have spent five minutes playing with balls to act this out, I realize that depending on the relationship between orbit direction and spin direction, we must either add OR subtract one revolution from the number of days in a year. And now that I have failed to find any provable answer to what that relationship actually is, I have to say that there are two possible answers for this puzzle, though neither is what one would immediately guess.

[Guest]

Zero

Spoiler for because:

366.25 + 1 = 367

Which is a prime number

Um prime numbers have 2 factors by definition, 1 and the number, so there are 2 factors...

[Prof. Templeton]

Um prime numbers have 2 factors by definition, 1 and the number, so there are 2 factors...

The Op says

Other than unity and the number itself, how many factors does this sum have?

So the answer is

Zero

[Guest]

The Op saysSo the answer is

Zero

argh.... sorry, blame the no caffeine....