A little over two years ago, while I was still an undergraduate student at Bangor University, David Crystal came around to give a talk based on his book By Hook or by Crook: A Journey in Search of English. One of the many adventures in language land he talked about was the hunt for isograms: words in which each grapheme occurs the same number of times. For instance isogram is a first-order isogram (or a 1-isogram), because each letter (i, s, o, g, r, a, m) occurs exactly once; deed is an example of a 2-isogram, since both d and e occur exactly two times. There are also a few examples of 3-isograms, such as deeded or geggee, but David was quite adamant that he did not know of any fourth-order isograms.
Naturally, this garnered my interest. It is certainly not a biggie to assume that order of isogram should be inversely related to frequency, i.e. 1-isograms will be quite common, 2-isograms somewhat uncommon, 3-isograms rare, and so forth; but a 4-isogram, while probably exceedingly rare, did not immediately strike me as something I would assume to not exist. So I went and googled isograms. A 4-isogram I did not find, but more questions I did.