There are many, many variables at play in this situation that pretty much makes the answer
any answer you want.
The walker counts less than the person standing still. How? Well, if someone enters the sidewalk at a point P where 0m < p < 20m along the walker's path after the walker has reached that spot, it is possible that this person will never be counted by the walker.
The walker counts the same as the person standing still. How? Assuming that people start on the sidewalk more than 20m away from the walker's starting position, the walker will always see the same commuters that the stander sees. The walker can ignore duplication, so they get the same count.
The walker counts more than the person standing still. How? Use the same scenario as the same count, but remove the assumption that the walker can differentiate between duplicates.
Of course, all of this requires that they are in the same general area. A sidewalk can be far longer than 20m, so the two can be potentially blocks away and still be on the same sidewalk. This means that they see different crowds and can have larger, smaller, or equivalent data sets.
Some variables that must be assumed to answer the question:
- The walker starts or ends at the same place as the stander
- The walker's speed.
- The walker's ability to match duplicates
- The ability of pedestrians to enter the path in the 20m range that the walker is covering.
- The fact that everyone is walking through the stander's field of vision, rather than behind them or exiting the path before they reach the stander.
Taking into consideration the OPs answers to the assumptions above, as well as extrapolations taken from the original source, the parameters sit as follows:
- The walker starts and ends at the same place as the stander
- The walker's speed is unnecessary, but he makes a number of complete loops and ends at the start point when the hour is up.
- Pedestrians can enter or exit the sidewalk at any time or location.
- The stander is in a doorway, so his view is completely unobstructed, and no one walks behind him.
Taking these into consideration:
We still don't have enough data to know who counted more
Let's take our three scenarios:
Walker sees more: Say fifteen people walk down the sidewalk in an hour. If three of them leave the sidewalk before they reach the stander, they will be counted by the walker and will not be counted by the stander. Thus, the walker will have a higher count.
Stander sees more: This logic holds true to my earlier statement. Again, say there are fifteen people on the sidewalk. If the walker passes the 5m mark heading toward the 10m mark and then a pedestrian enters the sidewalk at the 3m mark heading toward the 0m mark, the pedestrian will not be counted by the walker, but would be counted by the stander.
They see the same: This is the answer the book quoted in the question gives, and I would assume that it is the one OP wants. The basic premise here is that the walker will pass each pedestrian and count them once, whether it is coming or going. The stander will count each person as they pass by, thus giving them the same counts.
Here is the direct answer from the book quoted in the question:
Both of them counted the same number of passersby.
While the one who stood at the door counted all those
who passed both ways, the one who was walking counted all
the people he met going up and down the pavement.
There is another way of putting it. When the man who was
walking and counting the passers-by returned for the first
time to the man who was standing at the door, they had
counted the same number of passers-by - all those passing
by the standing man encountered the walk¬ing man either
on the way there or back. And each time the one who was
walking was returning to the one who was standing he
counted the same number of passers-by. It was the same at
the end of the hour, when they met for the last time and told
each other the final number.
This question goes to show how a good mathematical model needs to be very, very well defined. There are far too many variables that need to be accounted for here for us to be able to completely say who counted more, as there is too much chaos thrown in by the human element.