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Well, we made it. An easy flight from Seatac to Amsterdam, arriving at 7:30am. It was raining steady (it did so all day), so rather than cruise the town, we got a day room at the hotel right in the airport.
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At 9pm (13 hours after we got there) we got on a KLM plane for Cairo. It arrived at 2:00am. After clearing passport control, we were met by our driver and whisked to our hotel. Cairo is 5 million people and it already looks interesting. Our hotel is between fleabag and nice, but will serve our needs for 1 and 1/2 nights until we meet with the whole group.
Thanks for looking!