Level 20 last orange piece Thread - Beret

In the room that is encircled by the gravity slide I cannot get the orange piece.

I know what each of the platforms controls.

I think that the only way to get the medallion piece is to come from above which means hopping over the two green link blocks.
I think that you only need one of them to hop across- the left one. I could use the right one to pump up the low green platform in order to hit the green switch. Therefore, I would have to move the 4th blue platform down. This would move the lower green link block down and block the lower right pink platform from moving left and moving the two link blocks in the place where the blue platforms are. After a lot of thinking and platforming, I realized that the only way to make the many trips up and down that place is to use the upper pink platform to block the left high green link block (the one I was going to use to cross the gap) from going down when I use the highest blue platform to get up. However, I cannot get up to the pink block with only the right green link block.

Any help?

Ah, you're so close to getting it. Indeed, unless I'm misreading, you are correct in all your assumptions here except for one: do you really need to get up to the pink platform in order to move it far enough leftward? My guess is that you already know you can easily move it two spaces to the left. What would you need to have done in order to allow you to move it four or five instead?

Brilliant! Thanks so much NWK - that was just the hint I needed to crack that one

This is -- yet again -- such a well-designed puzzle: the way it at first appears you have four or five options for successful completion, but as you puzzle things through those narrow down further and further until the correct solution is apparent. What's so great is that one's earlier missteps don't feel like wasted time at all, because they end up being stepping stones towards the ultimate way forward.

The save-restore feature, is of course key to this being much less painful than it would otherwise be.

Yeah... I'm not seeing it. How can you pump up the low green platform? I can bring the green block to it, but then I would need a way to bring it back up, right?
I'm sensing there's something very obvious I'm not seeing here.

You don't need to bring the green block used to pump up the low green platform back up. You can make it across the upper place with only the first out of the two green blocks up there.

Yes, but what I mean is the green platform won't go forward as long as the block is resting on it... Or will it?

The lower green platform needs to be pumped up so that you can trigger it from inside the "shaft" with the 4 blue platforms. This is the only way to get through the upper right exit of the "shaft". To pump up that lower green platform you need to get the second green link block that is up high down in front of (NOT resting on) the lower green platform. THEN you can move the lower green platform and pump it up. You can move a platform forward if there is a block resting on it, but I don't see what that has to do with pumping up the lower green platform.

Got it! Thanks for the hints.
Again, a slight mistake made me think too hard: I had interpreted the above hints as "pump the platform with a green block", when in fact you are supposed to do it yourself (of course!).
I concur, great puzzle.