# Four letter words

Here’s another funny question about the English language: what is the sequence of three letters XYZ (where X, Y and Z are among the 26 letters of the alphabet) such that the number of correct (English) words of the form TXYZ is maximal, where T is just another letter? In this, it seems also best to assume that the last letter Z is not “s”, since the latter allows for many plurals of what are really three-letter words.

I think that, depending on the dictionary used (in particular, archaic words can be quite common among short words like this, and will only appear in the OED), the answer is between 13 and 17. The dictionary on my laptop (aspell-0.60-en) gives one word with 13 (say TWR), two with 12 (say BGA and IPX), and a few ending with “s”. The ending TWR jumps to 17 when permitted to appeal to the OED, and so does BGA. However, IPX only goes to 13.

Answers next week if nobody tries his/her hand first at the solution…

### Kowalski

I am a professor of mathematics at ETH Zürich since 2008.

## 7 thoughts on “Four letter words”

1. “ate” does quite well, although it’s not a winner by either of the measures you give: “?ate” has fifteen matches in the OED (? = bcdfghklmprsty), of which perhaps ten (? = bdfghlmprs) are common.

2. For the computer’s dictionary, ‘ate’ gets 10 words (certainly the common ones). In terms of commonness it seems the third of those I mentioned (IPX) is the best: the 12 words found by the dictionary are really common (and the last also, but as a person’s name).

Thanks for pointing out the ?abc searches in the OED, which I didn’t know about (so I was adding to the computer-generated list by searching each individual missing word, which does not take so long, but is not very efficient…)

3. Paul says:

May I suggest “?ear” for your IPX?

4. Actually, I didn’t know you could search the OED using strings like “?ate” — I searched each of the possibilities individually. My use of ? was purely as a compact notation.

5. So it’s amusing that the natural notation you came up with turns out to be actually usable in the online OED (and it’s really a nice thing to know…)