Do you need a Linux machine about as big as a few quarters? Man, have I got something for you. It's called the BeagleBoard PocketBeagle and it's the smallest Linux computer you can buy for $25.
I'm a huge fan of single-board computers for one simple reason: in my childhood, the technology that enables these things simply didn't exist. Further, a little kit like this one - complete with 512MB RAM, a tiny Octavo Systems OSD3358 1GHz ARM Cortex-A8 processor, and 72 expansion pins including power and I/O - is a true testament to the power of hobby electronics. About a decade ago getting something like this down to $25 was impossible. Now it's commonplace.
The PocketBeagle is completely open source and it includes an onboard boot ROM that will let you embed this thing into almost any project that needs a little Linux brain.
What can you do with this thing? Lots of stuff, as long as you know a little Linux and a bit of soldering. For example, you can boot directly to an SD card or via USB into an operating system and then power things like miniature satellites, drones, or even tiny game consoles. It's also a great learning computer. From the FAQ:
PocketBeagle is affordable, enabling you to dedicate one to live permanently in each of your different projects. Even though PocketBeagle is very low-cost, it is made with top quality engineering and manufacturing. In the unlikely event it is damaged due to misuse, it won’t cost much to replace. PocketBeagle will boot directly from on-board ROM that cannot be accidentally modified and will load software via USB, serial or microSD cards. A Chrome plug-in or cross-platform Node.JS Electron app can boot your board to add a Linux distribution to an attached microSD card. This means you can create reliably reproducible instructions on using the board, because it will behave the same way every time.
Now if they can just get this down to a size you can comfortably swallow, my plan for a Linux-powered in-gut classic games console can come to fruition.