Since it takes six man-days to dig a hole, it should take one man three days to dig half a hole, but you might object that you can't dig "half a hole", because that would still be a hole. However, a man can dig half a hole, it all depends on someone else digging the other half of the hole. And since you stipulated one man, he'll have to come back and do the other half himself. So it turns out it takes six days after all. First three days for the half he is digging, and then another three days to make the first half, well, a half.

Hole in the ground...deep subject!

or half a whole

Three of those men are shovel leaners, and the 4th does about 90% of the digging. Unfortunately one of the shovel leaners is the man that got assigned to dig alone, and while he is digging harder than usual, it's still never going to get done because he finds an excuse to do something else.

City employees, eh? ;)

No, Bank of America executives.

In order to dig half a hole, he first has to dig a quarter of a hole.
In order to dig a quarter of a hole, he first has to dig an eighth of a hole.
In order to dig eighth of a hole, he first has to dig 1/16 of a hole.
.
.
In order to dig 1/N of a hole, he first has to dig 1/2xN of a hole.

IOW, he can not even leave home, let alone find a shovel, or walk to the work site.

If he walks all the way around the hole, does he go around tha hole?

He goes around A Hole. Get it? A hole? ;)

Did we ever get correct answers for #36 and 37?

What if the hole digger was a shitman?

No, but you did get a correct answer to #21 though no one seemed to like it.
Also I am still waiting for an answer to the riddle
here are more answers:

I don't understand what the answer for #37 says. Is the answer 24 eggs?

Last weekend I bought a chemistry book like that - it's full of errors.

HLJ is correct. The book answer is in error.

I found a simple explanation elsewhere.

Given the initial statement:

3 hens can lay 3 eggs in 1.5 days
therefore
6 hens can lay 6 eggs in 1.5 days
and
6 hens can lay 4 eggs in 1 day
therefore
6 hens can lay 24 eggs in 6 days (already we see the error)
and
6 hens can lay 28 eggs in 7 days

A local college was looking for a way to help students decide between math and engineering majors. They headed the students to the large gym and lined up the girls on one side and the boys on the other. Then they told the students that they could walk half the distance to the other side every 15 seconds. When they reached their opposite number they could give them a kiss.

The mathematicians left knowing they would never reach the center. The engineers stayed knowing they would get close enough for practical purposes.