**damn = damn, damned = dammed, barred = bard, bass = base, jeans = genes, ruff = rough, phase = faze**. (The last three of these seem to me to be the ones that most people will find.) Like my proof,

*v*is the last generator to fall; they use

**chivvy = chivy**or

**leitmotif = leitmotiv**. I'm not sure how I feel about these; in both cases these seem like alternate spellings, not different words.

**veldt = felt**, as suggested by a commenter on the earlier entry, feels "right" to me; these are quite clearly two different words with different meanings,

**veldt**being a certain kind of open space in Africa,

**felt**being the stuff out of which the tips of markers are made. (I think this is the one I came up with the first time I saw this problem.) They don't seem satisfied with their proofs for

*v*, either; they introduce the space as a 27th generator, and use

**avowers = of ours**to show the triviality of v.

The paper in question is bilingual; the proof that the English homophony group is trivial is given in French, and the proof that the French homophony group is trivial is given in English. I particularly like the acknowledgements:

The third and fourth authors were partially supported by NSF and (by the results of this paper) numerous other government agencies.

A related problem is as follows: consider the group on twenty-six letters A, B, ..., Z with the relations that two words are equivalent if they are permutations of each other and each appears as a word in some dictionary of choice. Identify the center of the group. According to Steven E. Landsburg, "The Jimmy's Book",

*The American Mathematical Monthly*, Vol. 93, No. 8 (Oct., 1986), pp. 636-638, much work was done on this problem at Chicago in the seventies.

To get started: post = pots = stop = opts = spot = tops. Since post = pots, s and t commute; since pots = opts, o and p commute. This is clearly much harder than the homophony group problem. By the way, elation = toenail. (I've been playing lots of Scrabble recently; that set of seven letters seems to come up a lot.)

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