5 by 5
A Game of Logic for Late-Night Dining
By S. John Ross

This is one of my favorite pencil-and-paper "parlor games;" a game I've played with all of my friends for the last 25 years or so. Almost all of my really good gaming pals have sat up with me in the small hours of the morning, usually in a Denny's or donut shop or some other late-night dining spot, cursing over difficult letters and begging the waitress for pencils.

5x5 ("Five by Five," or simply "25" or even "LSD" when I'm feeling obscure) is a logical guessing game, a cousin of both hangman and Mastermind. I didn't invent this game - I first discovered it in a book of games and puzzles when I was in elementary school. I think the book was a little red paperback called Games for the Superintelligent, by Jim Fixx (the clever chap who started the jogging craze, and later fell dead of a heart attack while jogging), but since I haven't seen the book in over a decade, I could be dreaming it. The rules here are expanded and clarified from the version I learned years ago.

Anyway, here's the game. It's simple, sometimes maddening, and always diverting. Go grab a friend and try it out.

Setup

Each player needs a pencil and a piece of paper. Small note-paper is sufficient, usually, unless you write really big. It helps if each player writes the alphabet at the top of his paper - it's useful for keeping track of your progress. Before beginning play, each player must secretly choose and record a word. The word must conform to the following three rules:
  • The word must be "Scrabble Legal" - the standard set of rules for word games. This means an English word with no capital letters, no hyphens or apostrophes or other forms of punctuation, no funny stuff. An ordinary, vanilla word. There are millions of them to choose from, so this isn't much of a restriction.
  • The word must be five letters long.
  • The word must contain five different letters. So, "BEGIN" is a legal word, but "START" is not, since START has only four distinct letters: S, T, A and R.

You must choose a word which you are certain your opponent will be familiar with. 5×5 is a logic race; it's not fair (or very interesting) to win it by choosing obscure words. Usually, very common words are the trickiest to guess, anyway - the best words are those with plenty of common letters to confuse the guesser.

The Turn

Pick who goes first by fiat or by flipping a coin - it doesn't really matter; there is no particular advantage to going first (in fact, some prefer to go second, although there's technically no advantage to that, either).

On your turn, you must make a guess. This guess is another five-letter word, and it must also be "Scrabble Legal." However, it can include duplicate letters. The traditional first-guess words are START, BEGIN, and FIRST, but it can be any legal word you like.

Write your guess down. You'll want to keep a list of both your guesses and your opponents, in two separate columns.

Your opponent, after writing down your guess on his own sheet, gives you a number from 0 to 5. This is the number of letters that your guess has in common with his secret word. Mastermind players take note: The number has nothing to do with the position of the correct letters. Some examples:

TARGET GUESS SCORE
DOUGH DOWSE 2
STARE START 4
WHARF CLAMS 1
GRAIN CLOSE 0

Note that STARE and START share only 4 letters in common; the additional "T" in the guess START is simply ignored. Repeated letters can thus be used strategically to help eliminate or pin down particular letters.

Play continues in this way, each player guessing and responding, until somebody correctly guesses his opponent's word. Each player gets the same number of guesses, so if player One wins on his 10th guess, player two still gets his 10th guess, making tie games possible.

Errors

It will sometimes happen that a player realizes, deep into the game, that he has miscounted on one of his previous answers, and that his opponent is therefore playing with false information! When this happens, the "Error Rules" immediately come into play - the game is frozen until the Error has been corrected thus:

First, the player who made the mistake must correct it. Second, he must immediately grant a number of free "bonus" guesses to his opponent. These guesses are outside the structure of the normal game, and don't count as turns for the opponent. The number of free guesses awarded is equal to half the guesses the player has made since being given the false information, rounded up. So, if he hasn't made any guesses since the error, he gets no free guesses at all. If he has made 7 guesses since the error, he gets 4 guesses as his bonus, and so on. After the "penalty shots" have been taken, the game resumes.

Basic Strategy

When going from guess to guess, work in small, incremental changes from your previous guesses. If START got you a response of 2, and STARE gets you a response of 3, then you've got the E for sure. If you change more than one letter, the results will require extra, valuable turns to interpret.

Once you've eliminated some letters, you can use these "dead" letters to build words to test your theories. For instance, if you've eliminated C, G, H, I, K, N, P, R, T, and V, and know for sure that either A or E is in your foe's word, but aren't sure which, you can guess GRANT. Since you've already eliminated G, R, N and T, you know the response will be either 1 or 0. If it's 1, then you've got the A and eliminated the E. If it's zero, then vice-versa!

Once you've advanced in skill a bit, you'll find that knowing that either the A and E are in the word is often good enough . . . Rather than wasting a turn now to determine which, just mark the "suspect pair" and get back to it later if you need to. In the meantime, work on the other letters - having pairs can often lead to intuitive leaps that can win you the game!

On average, a skilled 5×5 player will guess his foe's word on the 10th or 11th guess - quicker than that is very good, and too much slower than that will make you shark-bait for the experts! A well-chosen secret word, of course, can make a difference of a turn or two, and that's all the difference in the world, in 5×5.

[Graphic: The Astonishing Creation That is the 5x5 Sheet]
The 5×5 Sheet

While any old notepaper will do, I've prepared a handy 5×5 Sheet, in Adobe Acrobat (PDF) format (in a 7k downloadable ZIP), for those who like to print out reams of stuff. It has space at the top so you can fold a flap down for privacy (essential when playing across the table at Denny's), a big box for your word, five smaller boxes for the letters in your foe's word (as you deduce them) a handy alphabet (in case you forget how it goes) and dividing lines.


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