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Sausage's Hybrid Speed Solution
Step 1 - Forming the Cross

That's better. Our first task is to move the BLUE and YELLOW edge piece to the BLUE face. Turn the RED face clockwise once:
The piece is now joined with the BLUE centre. Turn the BLUE face clockwise once to position is against the YELLOW face as well:
This will help us to guide the other three BLUE edge pieces into the correct place. Next, notice we can spot the second edge piece to go to the BLUE face. We can see it has a BLUE sticker, but we need to find out what the other colour is too. A quick peek around the corner will reveal that it is ORANGE in this case. On this cube, ORANGE is opposite RED, so turn the BLUE face once clockwise (you'll see why in a sec)...
... to here. The RED and BLUE edge cube has shown up. Ignore it for the moment. Let's have a peek around the corner to show you what's about to happen:
Now, turn the green face once clockwise to send it up to the BLUE face:
Great. It's there. Only two more BLUE edges to go. We'll tilt the cube slightly and view it from another angle...
The RED and BLUE edge is the next one we can easily see, so he can be our next target. He's already joined up with the BLUE face, but he's around the wrong way (he's flipped).
A turn of the RED face anti-clockwise will get the RED and BLUE edge momentarily away from the BLUE face. If we turn the YELLOW face once anti-clockwise, it will join up in BLUE face correcly. One word of warning though... the BLUE edges must go into the BLUE face but they must also line up with their other colour in the other faces that surround it, just like what we did woth the YELLOW and blue edge. Anyway, you'll see... let's move this YELLOW face once anti-clockwise...
Great. Three BLUE edges are now in. And the BLUE and GREEN edge has shown up. It must have been hiding on the bottom. We can also easily get this one to the BLUE face, but first we need to make a space for it by turning the BLUE face once clockwise:"
Good. This has now created a "gap" that will allow us to move the BLUE GREEN edge piece in. We can do this now by turning the YELLOW face once anti-clockwise...
Well... it's in... we have a cross. We just need to make a quick check to confirm that all the BLUE edges are in the correct order. Turn the BLUE top face until the other colours in the BLUE edges line up with the other faces:
See how they line up with other face centre cubies? If they don't, then you got the order wong. You'll need to swap the pieces around to get them in the right order. I'll turn the colours all back on again to show what your cube might look like at this stage...
It's still a bit of a mess. But it's got the cross built. Time to go to step two. We'll turn our whole cube over and start at the other end... but before that, we need to make up a story...

Move to step 2.
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