## Tuesday, January 6, 2015

### Think: The Five-Letter Word Game

Linda taught me this game when I was visiting her in Muskegon. She just called it "the five-letter word game." I thought it needed a name, and Think is as good as any.

Preparation
Each person thinks of a five-letter word with all five letters different, and writes it down in a hidden spot.

Goal

Play
The players take turns offering a five-letter word (all letters different), as guesses, and as clue-gathering. If the guess is not the right word, then the opponent tells how many letters are right.

The game is similar to mastermind, but there's no information about where the letters go. (So you could get all five letters right, and still have the wrong word!) It's not a math game, but it is a logic game, and I think logic and math are twins.

Example
I'll share my guesses:
STOMP 0 (No letters right. Great. I can cross all of those off my alphabet where I'm keeping track.)
BLAND 2
QUOTE 1
FLASH 2
DIRTY 1
TRUCK 0 (Now I know 9 letters that aren't in the word.)
VOWEL 2
EXITS 2
QUICK 1
LARDY 2
BINDS 1
NIGHT 2
LINER 3

Would you have picked other clue words? Do you have enough information from these clues to guarantee any of the letters in the word?

1. This game used to be sold under the name "Jotto". For 5 letters, I need to be able to keep notes. But the same game using only 3 letters (4 if you're really ambitious) can easily be played without any note-taking and, in pre-smartphone days, used to be a family favorite to kill time while driving or waiting in line. Here's a write-up of one particularly memorable session: http://okasaki.blogspot.com/2008/04/games-for-programmers-jotto.html

2. I love your post! Yep, this looks like Jotto. But I like my name better, since it's a legal word in the game. And I like your version too.

3. Yes, growing up in the midwest (1950s), "Jotto" was our favorite family game (even though we knew of no other households familiar with it). Great game, that can be played online now, but I've not seen it in a store in forever. BTW, in the original game you could choose 5-letter words with multiple same-letters, like "state" or "puppy" which made for deliciously-difficult games.
Anyway, you brought back memories!

4. Glad to bring back memories, Shecky.

Anonymous, can you tell us how you got that word?

5. I'm trying to think of a useful way to organize the information you get at each guess. Still no great approach.

My temptation following STOMP would have been to pursue 2 letter modifications, like
SWAMP
SLUMP
STOCK

Though this seems similar a strategy mentioned in Chris Okasaki's blog that he declares sub-optimal.

6. Some further thoughts. Spoilers if people don't want to know:
TRUCK 0 and QUICK 1 implies QUI 1. Since Q needs a paired U, QU being correct means 2 right, so we have UI 1, so either U or I are in the final word.
STOMP 0 and EXITS 2 implies EXI 2.
TRUCK 0 and LINER 3 means LINE 3.

This gives us the following possibilities:
U (not I) then EX and LN, so EXLNU. Doesn't fit with LARDY 2, so we conclude I is a letter, not U.
QUOTE 1 then means E is a letter, so we have E, I + {L or N}.
DIRTY 1 and LARDY 2 means we must have L.

Now, we're at E I L.

BINDS 1 and BLAND 2 implies A.
FLASH 2 and NIGHT 2 implies G.

Now, we have E I L G A.

7. I organized the information visually in an array with the letters of the alphabet along the top row. As I listed each word (with the number of correct letters) on a new row, I put a dot under the letters that the word is composed of. When letters were eliminated, I crossed off the dots in that column. After STOMP and TRUCK eliminated UOT, the only letters possible from QUOTE were Q and E, and Q would be unlikely without the U. Therefore, one letter is (most likely) E. I circled the E column so that when I continued to list words, if I put a dot in the E column I knew that one letter of the new word listed was already spoken for. I continued filling in information on the chart, and didn't have any new leads until QUICK. (Actually the first time I worked it out I accidentally skipped over the word QUICK, which made it a bit more complicated, but still solvable!) Continuing with the assumption that Q was eliminated due to no U, the next letter must be I because C and K have already been eliminated. I circled the I column in my chart. Now, looking back at the word DIRTY, I eliminated D and Y.Since D, R, and Y have been eliminated, then LARDY gives us both A and L. I circled those columns.Now looking back and BLAND, I can eliminate B and N. Looking back at FLASH, I eliminate F and H. Looking back at VOWEL, I eliminate V and W. BINDS gives no new information since I already know I, and the other letters have all been eliminated. NIGHT gives us the G since N, H and T have been eliminated and we already know I. We now have 5 letters, A, E, G, I, and L, and playing around with them a bit leads me to AGILE. We don't need to use LINER, but it's a good confirmation. Sorry if it was a spoiler! I'm happy to email you my chart if the explanation was confusing. Fun game!