traveling economically

This is a case where you have to do your own homework. There is no pat answer. And you need to try a number of combinations. Use any of the big search engines and plug in Seattle,London,Berlin,Manchester,Seattle and see what you get. Then try Seattle, London, Manchester,Seattle. You can then price London/Berlin and Berlin/Manchester using budget airlines and see what you total cost will be. You almost always save money using open-jaw tickets.

EasyJet.com flies from Gatwick to Berlin Schonefeld Airport, and that'd be your best way to go.

You can also fly back to Manchester directly from Berlin Schonefeld Airport on EasyJet.com.

Using Kayak and dates in May, I found a lowest fare for the Multi-city trip (SEA to LHR to BER to MAN to SEA) as $1908 on British Airways. The flights from Berlin to Manchester and Manchester to Seattle are not direct, you change planes at Heathrownin each case.

Using the same outbound and inbound dates in May, the round trip flight SEA to LHR and back on BA is $1212. (you can go on Air Canada for $15 less, but that requires a flight to Vancouver, not worth it in my opinion). I didn't price the EasyJet flights from Gatwick to Berlin and Berlin to Manchester, but I am sure it is way less than $700. You can go from Manchester back to London by train if you want. Tickets are cheap if bought in advance. Or fly back from Manchester on BA via London for $1193---less than the LHR round trip costs. That would be my choice ( assuming you don't want any more time in London).

Today, using made up dates in May, I found a price of $1502 for SEA to LHR, LHR to TXL the next day, TXL to MAN (via LHR) 6 days later and MAN to SEA (via ORD) the next day. All flights are badged American Airlines, but all but the MAN to SEA home are actually operated by British Airways.

Since you did not give specific dates, the prices might change when you do it. Go to ITA Matrix (http://matrix.itasoftware.com/) and use the multi-city tab to do your searching. When you find something suitable, print the itinerary results. You can also explore the multi-city option of flying to LHR and back from MAN as one trip and within Europe (LHR -- TXL -- MAN) as another and see if it is cheaper or worth doing.

Then you will have to contact the specific airlines (sometimes calling is best) to book the reservations. With the print out in hand you will have all the code numbers to give to the agents to get exactly what you want.

Yes prices are different for different days, depending on how many seats remain tobe sold and other factors. You cannot see the grid displaying prices for multiple days in each direction if you do a Multi-city search. So I like to use the main longhaul'flight alone to find out which days of the week are less expensive. Mathis should appear as a grid on either Kayak or ita matrix. if your trip dates are even slightly flexible you could try that for the SEA-LHR-SEA part and then use what you learned to book the complete trip.

Actually on the ITA Matrix search, you can adjust the dates a little even with the multi-city search. The default for each leg of the journey is "on this day only" but you can click on the drop down box and get as far out as "plus/minus 2 days." That will give you the date you put in the box with 2 days before and 2 days after, making 5 days. Depending on what your "middle" day is, you may or may not have price changes for the days before or after it. The results are in a list and it's not as cool as a month long grid, but it helps.