Story highlights CNN's Al Goodman spent time in the transit zone of Moscow's airport

Edward Snowden is believed to be in the transit zone

The zone can include other locations in Moscow

The maximum stay allowed is 24 hours

It seemed like an exciting assignment -- go to Moscow on the trail of former NSA contractor Edward Snowden.

After acknowledging that he leaked details to reporters about a massive U.S. government surveillance program, Snowden reportedly arrived at Moscow's Sheremetyevo Airport on a flight from Hong Kong on June 23, and settled in at the transit lounge.

But he has remained out of sight. Could I find him?

Would he be browsing the duty-free shops, amazed at the sheer volume of magnum bottles of liquor for sale?

Would he be sipping cappuccinos in the coffee shop, miffed that they cost 5 euros, or $6.50, each?

Determined and anxious, I flew in under the cover of darkness on an overnight Aeroflot flight from Madrid, arriving at 6 a.m.

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The passport control officer told me to wait. "Sit over there," she said, and walked off with my documents. Hmmm. Would I end up in legal limbo like Snowden, whose American passport was revoked by Washington, making it difficult for him to cross borders?

Well, no. After about 10 minutes I was waved through, and got out of there so quickly that I forgot to ask the passport officer if she'd seen Snowden lately.

But there was no entry stamp to Russia in my passport. Because, like Snowden, I had not officially entered the country; instead, I was now in the lounge for passengers who are just transiting through, along with those who enter the area to board departing flights.

It's a truly international place, filled with a broad swath of humanity. Citizens from the Russian Federation, Europeans, Asians, a small number of Americans and some Cubans. Young backpackers and rich business executives. Exhausted parents with children, including a brave little boy whose legs appeared disabled, struggling to take every step, squeezing his mother's hand.

All trolling the transit zone, with its gaudy emporium of high-end shops wedged next to mom-and-pop trinket stores that sell souvenirs seemingly left over from the old Soviet Union, including a fold-up metal drinking cup, which I couldn't resist.

There are coffee shops that offer Russian pancakes and Wi-Fi, and charge in rubles, dollars or euros. There's even a Burger King and a TGI Fridays.

In this enormous transit lounge, Snowden surely has plenty of places to hide.

Its three terminals -- D, E and F -- form a very long, curvy rectangle, with 60 boarding gates, and flights to a lot of places that Snowden can't go, for fear of being caught.

Western Europe? Not a good idea for him to fly to Paris or Berlin. New York is obviously out of the question.

Tokyo or Shanghai? Nyet. Nor Tel Aviv. Even Baku, capital of Azerbaijan, is probably risky.

There is an Aeroflot flight to Havana, with connections to Venezuela, a country whose leftist government has offered asylum to Snowden.

On a Friday, my first day in the transit zone, there was no Havana flight to keep an eye on, which gave me a chance to explore.

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Russia and other countries can designate various locations and settings, even outside of the airport, as the amorphous transit zone. There could be detention areas, medical facilities, or other locations in Moscow given that designation -- so Snowden could be miles away from the airport but still in "transit."

One part of the Novotel, not connected to the terminal but visible from it, is part of the transit zone. I decided to see whether Snowden was holed up there.

I reserved two rooms -- one for me, the other for a CNN camerawoman who came from Berlin.

Aeroflot ground agents directed us to a bus, which rolled across the tarmac as, officially, a moving part of the transit lounge. So we were leaving the airport in Russia -- but staying in the "zone."

Accompanied at all times by minders, we checked in and were directed to the second floor, the secure transit zone floor.

The guard in the hall made sure we didn't go down to the lobby or gym or to other floors. The only way to get food was from room service, which is actually not such a bad idea.

We walked the hallway. Snowden could have been behind any of the 40 room doors on the second floor. He did not come out.

At 4 a.m. the next day, we left the hotel, accompanied at all times, until we were back in the airport terminal transit lounge for our departing flights.

The rules say you can stay a maximum of 24 hours in the transit lounge and then must leave on a flight. We did.

But Snowden has apparently been in the lounge for nearly three weeks. How does he do it? I would need a second trip to find out more.

A few days later, I was back, this time alone. On the second trip, you begin to feel like something of an authority on the transit lounge.

Snowden reportedly is traveling with several laptop computers. If they're heavy, he's got a problem. So did I. There are hardly any luggage carts in the transit lounge. I finally found one, and then a woman from India followed me around until I was done with it.

I searched again, up and down, and when it got to be 12:30 a.m. -- when there are no flights for several hours -- I checked into the Capsule hotel in Terminal E, renting a tiny room for the minimum four hours. Didn't see Snowden there either, nor back in the terminal, starting at 5 a.m..

I figured the best shot was the Havana flight, leaving at 2:05 p.m. It's no secret that observers are closely watching that flight. I went quite early to the boarding gate, number 22 in Terminal D. A couple of guys with beards looked vaguely like Snowden. But no, one turned out to be Danish, the other Russian. I approached both. They laughed. The Danish man said I was the second person to ask him that.

It was boarding time. A veteran Russian photographer and I were working the scene. There was a lot to monitor -- the passengers getting on at the gate, the stairway from the tarmac up to the boarding walkway, for crew and possibly someone else, and a terminal elevator, inside the secure zone, from which someone might be hustled aboard down the walkway.

Watching all this -- and, it also turns out, watching us -- was a mysterious, middle-aged burly man. As the boarding was in progress, he made a mobile phone call, reporting back to someone -- in Spanish -- that two photographers were taking pictures.

After the boarding finished, and the plane was about to push back with no sign of Snowden, I approached the burly man. I asked him, in clear Spanish, if Snowden was aboard. He pretended not to understand. I repeated the question in Spanish. He again feigned inability to speak Spanish. So I asked him in English. He replied that he didn't know.

Could he have been from Venezuela or Cuba? He didn't say.

At least I could see and talk to the burly man. So far, I haven't been able to do that with Snowden.