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Tuesday, May 16, 2006

Word puzzle

Think of a two-letter word, such that when the letters are reversed, a new word, commonly used, is made. (Example: start with the opposite of "off.")

OK. Now think of a three-letter word that has letters that can be re-arranged so that you can make three or more distinct, relatively common, three-letter* English words out of them. (No proper names, such as Joe, allowed)

Can you think of a four-letter word that has letters that can be re-arranged so that you can make four or more words, using the same constraints? How about a five-letter word with letters that can make five or more words, six, etc.? Post your answers as a comment.

I found three-letter and four-letter in a few minutes. I didn't find five- and six-letter words that fit, at least not yet.

There are only two possible arrangements of the letters in a two-letter word. There are six arrangements of the letters in a three-letter word, provided they are unique. (The first one can be any one of the three, then the second either of the two left, then the third the remaining letter, so the number of possibilities is 3 x 2 x 1, or 6.) By similar reasoning, there are 4 x 3 x 2 x 1 = 24 possible arrangements of four unique letters, and 5 x 4 x 3 x 2 x 1 = 120 possible arrangements of five unique letters, and so on.

Try it! Thanks for reading.

*Katherine spotted a misprint here, which I have corrected. Thanks!


Anonymous said...

Five letters: steam, tames, mates, meats, teams. Six letters -- uh, not yet.

I thought of a similar puzzle once:

Start with a one-letter word.
Add a letter and find two words.
Add another letter and find three words.
Repeat the process until you get utterly frustrated.

I got to five letters (though I cheated at the 3-letter stage and allowed a familiar acronym).

Anonymous said...

3: ate, eat, tea
4: diet tied tide edit
5: peals leaps pales lapse sepal

This is presuming you mistyped and meant "three-letter English words" in your second paragraph (not four-letter).

Anonymous said...


Martin LaBar said...

Thanks. Here are my solutions:

no, on

are, ear, era

vile, evil, veil, live

pears, spear, rapes, spare, reaps

That's as far as I got.