Timbo's puzzle

[Rene]

Fibonacci, here I come!

For Sixteen (rabagot): gepyceb

[Twee]

Here's my belated entry for "without barrels" (gegecif): xolicaz It's kludgy, but doesn't rely on probabilities, and doesn't fail on any case. Now if i can just figure out how Bucky's solution works.. 

Edit: I was really proud of this solution until I looked at Jf and Renes' solutions. Jf solved by the same strategy but with a much more compact machine; whereas Rene's solution showed me just how much I overcomplicated the problem. I get to enjoy a laugh at myself at least.

[Bucky]

Here's my belated entry for "without barrels" (gegecif): xolicaz It's kludgy, but doesn't rely on probabilities, and doesn't fail on any case. Now if i can just figure out how Bucky's solution works.. 

It works on the principle that only the last crate on the matcher matters.  As long as my machine in the upper-left corner only spits out the correct crate after a certain point, it solves the problem.

You can ignore the pile of barrels and crates that get dumped through the system at the beginning - they're just for fun and get incinerated anyway.  The three critical parts of the machine are (from top to bottom)
Warning:The spoilers will deprive you the rewarding experience of figuring these devices out yourself.
A trick for moving a ? crate without forcing it to a value.
A compact filter which will eventually produce an F crate directly above a copier
A transcribing device which, given a steady supply of F crates, will send a stream of crates down the pipe that have the same value as the barrel provided by the puzzle

[Twee]

It works on the principle that only the last crate on the matcher matters.  As long as my machine in the upper-left corner only spits out the correct crate after a certain point, it solves the problem.

Thanks! I'd already figured that out shortly after I made that post. However, I just took another look at your machine and I intend to steal your "transcriber" for future solutions. Its much more compact than what I have been using: A device that drops a stream of crates or barrels starting at F and incrementing down by one which required about 8 empty spaces between it and the target.

[Twee]

For "One Bit I": (fygicyr): xigotyz
This one felt like kind of a watershed to me. I wish I'd savored my sense of accomplishment a bit longer before looking at "One Bit II" though.

[immibis]

For Without Barrels: piryxuk