Words & Stuff

v: The Game of Fives

(1 June 1997)

(Note: You'll need a browser that can display tables to get the most out of this week's column. Apologies to those without such browsers; formatting the game without using tables would have been a pain, and would have looked rather ugly.)

There's a game I learned in fifth grade that I've never encountered since; lacking any other name for it, I call it "Fives." One player (the chooser) picks a five-letter word with no repeating letters and draws five long dashes, one blank for each letter. The other players attempt to guess the chosen word.

Each guess consists of a new five-letter word with no repeating letters. The chooser determines which letters the guess has in common with the chosen word. Under the blank for each letter in the chosen word that's the same as any letter in the guess, the chooser writes the guess word.

The game works a little like the well-known commercial game of Mastermind®, except that guessers are only given one type of information about each guess -- as a guesser, you know only that one of the letters in the guess is in the given position in the chosen word. (You're never told whether a letter in the guess is in the same position as a letter in the chosen word.) Subsequent guesses help to narrow the field until you arrive at the correct word.

An example of play to clarify the above description:

Martin, the chooser, picks the word "fives" and writes five blanks.

 _____  _____  _____  _____  _____

The players begin to guess words.

Naomi: shire

Martin notes that "shire" shares three letters with "fives," and writes "shire" under the blanks for the I, the E, and the S in "fives."

 _____  _____  _____  _____  _____
shire shire shire

Now the guessers know that one of the letters in "shire" goes in each of those blanks, but don't know which letter goes in each blank.

Otto: wakes

 _____  _____  _____  _____  _____
shire shire shire
wakes wakes

The guessers can now see that the last two letters of the chosen word must be either ES or SE, since E and S are the only two letters that "shire" and "wakes" have in common. (EE and SS are ruled out by the no-repeating-letters restriction.)

Naomi: smith

 _____  _____  _____  _____  _____
shire shire shire
wakes wakes
smith smith

Clearly the final letter of the chosen word is S (the only letter that "shire," "wakes," and "smith" have in common). The fourth letter must thus be E. Since S is already being used, the second letter must be either H or I. The guessers can also see that the first and third letters are not any of the letters in the words guessed so far -- A, E, H, I, K, M, R, S, T, W.

Otto: black
Martin: No change -- none of those letters are in my word.
Naomi: chafe

 _____  _____  _____ E S
shire shire shire
wakes wakes
smith smith
chafe chafe

The second letter, since it was known to be either H or I and is not in "chafe," must be I. Since words containing C, H, A, and E have all been guessed and were not listed under the first letter, F (the only previously-unguessed letter in "chafe") must be the first letter, making the chosen word FI_ES. The third letter can't be A, B, C, E, F, H, I, K, L, M, R, S, T, or W, since all of those letters have been part of guessed words that weren't listed under the third blank; so the chosen word must be "fines," "fixes," or "fives," and guessing each of those in turn reveals which it is.

I always intended to write a computer program to play Fives, but never got around to it; I got bogged down in compiling a dictionary of useable five-letter words (this was in the days before I knew about searchable online dictionaries/word lists and regular-expression matching). I suspect there's a way to guarantee the minimum possible number of guesses in determining the chosen word, but I don't know what that approach would be offhand... Suggestions welcome.


Mastermind is a registered trademark of Invicta.


Jed Hartman <logophilia@kith.org>