Walking the dogs yesterday, cool and mostly clear mid-afternoon near KHVN and saw a few aircraft heading SSW from NNE. When I’ve been able to check, these are usually flights from Europe to Florida or the Caribbean. Very pretty as they were leaving very crisp contrails and the aircraft were bright from the low Sun. The last one I saw was curious because it was a quad jet but only had three contrails. The two from the right wing very distinct but only one on the left. It wasn’t directly overhead, maybe a few miles South so I thought it might be the angle but I watched it for 5 minutes or so and they never split on the left. I am not a pilot just an enthusiast so that got me wondering, other than a failure would a quad jet ever be run on three engines intentionally? Thanks
I’m not sure about what you saw, I would have suggested an engine testbed, such as GE’s N747GE. But that seems unlikely given your location. Although, I remembered back to hearing of a BA 747 running on 3 engines for just about all of the flight. You can read a bit more about that here en.wikipedia.org/wiki/British_Airways_Flight_268
Obviously this is not an optimal procedure, and I think having the engine windmilling (turning as air passes through it, even though it is not turned on) may cause damage. The reason I say this is 747-200s and 747-300s could carry engines underneath the wing, and had a shield fitted inside the spare engine, to stop them turning over. Search “747 spare engine pod” to see some interesting photos. There was also a case where a 747 flew with only 3 engines attached, you can see a photo here Airliners.net
I’m not a pilot or aircraft engineer, just an enthusiast, these are just things I recall after a lot of reading. Hope it helps! 
I have seen four engine jets at cruise, and sometimes it appears that one contrail comes from one side, and two from the other. I don’t know why, maybe because of the way the air rotates as it comes out of the engines and off the wings. But to answer the last question, no, a jet airliner would not intentionally cruise on three instead of four, because that would most likely result in burning more fuel. There wouldn’t be any reason to do so.
Thanks. I couldn’t think of a good reason but I couldn’t be sure. Must have been just the wrong angle I guess.