Shown here is a crude but functional homemade transistor from 1948, from the October 1948 issue of Radio News.  While the author had not yet used the fragile device in a working circuit, he did note that he achieved amplification by a factor of up to 50.  The transistor was very unstable at that high amplification, but it did work reliably amplifying by a factor of 15.

The transistor was made of a 1N34 germanium diode carefully broken open.  One lead was kept intact, and the other two contacts were made by making cat whiskers out of filaments of old tubes.

The article cites some 1920s articles where the authors made “amplifying crystals” by a similar means.  By applying the techniques in this article, the advanced student could prepare a science fair project that his or her teacher would probably declare impossible–making a homemade transistor.