I had a look at Tinycore linux distro which is only
10MB. Tiny Core Linux is a very small (10 MB) minimal Linux Desktop. It is based on Linux 2.6 kernel, Busybox, Tiny X, Fltk, and Jwm. The core runs entirely in ram and boots very quickly.
http://www.tinycorelinux.com/I ran it in 'VirtualBox' as a virtual computer and it ran ok, you could load it on a usb stick and take it with you..