Q:

If everyone in the world disappeared except 35 random people, how long would it take for one of them to realize they're not alone?

Everyone suddenly disappears from earth except 35 people randomly scattered wherever they were before everyone disappeared. How long would it take on average for 2 or more people to meet? What other factors would indicate to a person that they're not the only person who didn't disappear? 

A:

Assuming that it's purely random, let's consider where these people would probably be. Taking the percentage of the population each country represents, we get:

China: 18.2% = 6.37 people
India: 17.5% = 6.125 people
America: 4.29% = 1.5 people
Indonesia: 3.43% = 1.2 people
Pakistan: 2.78% = 0.93 people

...etc. The percentage keeps going down. This means that roughly 6 people will be in China and India, each, and then the next 7 countries or so will probably have 1 survivor each (maybe 2 for America). The other 15-16 survivors would probably be found somewhere in the next 25-30 countries (as the probability of having any survivors approaches 50% or less).
So really, our most likely candidates for people meeting each other are China, India, and Europe (9.83% of the population as a whole for probably 3, maybe 4 survivors). 
For India, 72.2% of the population lives in 641,000 rural villages, and this population is pretty evenly distributed, meaning 4-5 of our 6 survivors are probably located on a unique patch of 650-820 thousand square kilometers (3.2 million square kilometers divided by 4-5 people). This means they could walk for 800 kilometers in any direction, and never see each other. 
The only real chance that they'd ever find each other would be if they all decided to go to the same major city. But which one to choose? There are 53 cities in India with over 1 million people, and at least 8 with more than 5 million. Would someone in the populous region of Bihar go the 1300 km to Mumbai, the biggest city, or the 800 km to the capital of New Delhi? If you go to the wrong city, will you travel another several hundred km to a different city and hope your luck gets better? Most people are more likely to go to ground, either before any travel, or after failing to find someone after travelling once.
And even if two people, by chance, happen to go to the same city, it would be rather unlikely that they'd run into each other. Let's take Mumbai, for example. It has an area of 603 square km, which increases to almost 4400 square km including the metropolitan area. This means that two people would have to run into each other in an area that is roughly 25-70 km across and deep.
Chinese survivors have the advantage in that their population is concentrated in cities, but with a maximum metropolitan area holding only about 3% of the population, the survivors are still likely to be scattered all across China, or at least the eastern half, which still has an area of about 4 million square kilometers (greater than that of the entirety of India). The issues with choosing a city are also present for survivors looking to migrate, as Shanghai, Nanjing, Beijing, Hong Kong, Guongzhou, etc. are all major cities.
For Europe, this only gets worse. The area expands to 10 million square kilometers, and unlike India or China, which have their own capitals that could act as a rallying point, each country in Europe (which would probably have at most one survivor) would probably attract survivors to their own capitals. A single German survivor, for example, would likely head to Berlin rather than Paris.
So in summary: most survivors would probably be scattered over an incredibly vast area (hundreds of thousands to millions of square kilometers for a single person); if they decided to go to a big city to intentionally look for other survivors, there's a good chance they'd go to different cities than each other; and even if two survivors both decided to go to the same city, finding another person in even the same city is rather unlikely.

A:

It's HF radio, or nothing
The odds of anyone meeting again are almost exactly equal to the odds of at least two being either radio hams, or able to learn the skills from books.
The population density of 35 people worldwide is so extremely low that the odds of finding someone without the benefit of global communications is practically zero.
Strategies like finding a printing press and posting thousands of fliers in different cities are a bold try, but they are hopeless: they fail to grasp the massive scale of the task. You could distribute 100,000 fliers in each of a hundred cities: and your odds of finding someone are still very, very long.
So it's global comms, or nothing. 
Internet comms could work, but you have a matter of at most a few days to sort yourself out before the system fails. Act quick: find someone, somewhere, amidst all the autogenerated cacophony and BS, in the next three days. Time's up.
HF radio, on the other hand, is highly resilient, extraordinarily efficient global communication system. It can remain operational until you run out of spare parts -- the power requirements for QRP operations can be met by solar, batteries, or even pedal generators. There are standard hailing frequencies, standard protocols. Including standard protocols for global catastrophes. You might not make contact the first time you try, but if you keep trying, it approaches certainty.
Yes, HF radio is a skill. But you have the rest of your life to learn it, or die alone.

A:

This is an interesting question.
Obviously, just walking about and hoping to meet someone is fruitless, the chances are just ridiculous. What you would want to do is communicate. Now we know how many people survived and what the likely distribution is, but they do not.
From the perspective of a survivor, everyone around is suddenly dead or disappeared. Unless you are criminally stupid, your first thought will be about survival. Short-term that is not a problem, go into an empty shop and take what you want. Mid-term you are down to canned food. Long-term, you are going to have a serious problem.
So you want to get to a city edge and set yourself up there - with both farmland and supply depots (aka supermarkets and other shops) within reach. That also means that - at least at first - the city center is just a quick drive away, provided that whatever catastrophe took everyone else left the roads useable. Since you don't know if there are other survivors and how many, you would pick a landmark site, something others would think about as well, and post a written notice there. This is easy, low-cost and thus something that makes sense to do "just in case", even if it is fruitless you didn't invest much.
You would also post on FB, Twitter or whatever websites your frequent, just out of habit "hey guys, what is going on?" and for the same reason - it is easy.
Most of the answers so far assume too much knowledge and thus targeted activity on the side of the survivors.
The Internet would probably be down by the time you start any targeted activities, as pointed out in other answers.
Your billboard notice is a gamble, but you don't know the odds. It is, however, the most likely thing to work, as it is intuitive and doesn't require to people to be in the same place at the same time. Especially if people go roaming, there is actually a reasonable chance that they would meet. Let me explain:
Once you got the survival thing down, you are left in a world with plenty of cars and practically unlimited fuel - for a time. Current fuel goes bad in about a year, and the cooling etc. required to keep it longer will fail together with the electricity.
Once you realize that a) there are very few other survivors, if any and b) survival alone is much more difficult than in a group, the logical next step is a game of "what would the others do?"
And I believe it is trivially obvious that everyone would head to the nearest largest city. The capital. Leave a message there, in a central place. In Europe, you would take a car and drive to Paris, post your notice at the Eiffel Tower. Then drive to Berlin, post at the Brandenburger Tor, and so on. Invite others to leave their messages so you know someone else is alive and then POST YOUR ROUTE. Make it a circle through the 5-6 major cities in the area and drive it two or three times. You can easily cover the distances (again assuming roads are free) in 1-2 days. You can do this early when supplies are not yet an issue.
If after 3 or so rounds you see no notices and nobody waiting for you at the next stop, assume the entire area is empty and go elsewhere. If you start out in the Americas, good luck. If you start out on an island, go farming and enjoy the rest of your life.

