I have a system with 32 MB of RAM. I am wonding if Tinycore will run on it?
Using the "embed" boot code should allow you to boot on a 32 MB machine, but the skimpy RAM will probably prove inconvenient before you get much done.
Setting up some swap space would be helpful.
Also, "mount" your extensions instead of "install"ing them.
To save a little more RAM, use Microcore and add the core elements and window manager as "mount"ed extensions.