Puzzler Magazine of 1929
seeks 3x3 magic word square from "temporary"

This page provides my analysis of the puzzle Will Shortz gave to NPR listeners on 2003-11-30. If you would like to subscribe to my free email list to get a synopsis of this puzzle segment each week, send a blank email to: nprpuzzle-subscribe@igc.topica.com

Here is this puzzle:

Last Challenge (given 20031130)
Will reports that he got this puzzle from a 1929 issue of Puzzler Magazine. Unfortunately, the answer was in the next issue, so Will had to solve it himself. Take the letters of the word TEMPORARY. Arrange them in a 3 by 3 square so that each of the acrosses, downs and the two long diagonals spells a word. Each of the diagonals must read backward as well as forward, making 10 words to be spelled altogether. All the words are common and uncapitalized. What is this special square?

Actually, it should be obvious that if there is one solution, then there must be two (unless three of the 9-letter word's letters are repeated within the 9 letter; then the magic square could be its own mirror image [see "hortatory" below]):
MOP
EAR
TRY

and

MET
OAR
PRY
The two solutions, of course, are reflections of each other on the NW to SE diagonal. Each solution makes the following ten three-letter words: MOP, EAR, TRY, MET, OAR, PRY, MAY, YAM, TAP and PAT. By my check of all possible permutations of TEMPORARY, these two are the only solutions using the Official Scrabble Dictionary list of 977 acceptable three-letter words.

Since I had the program all written already, I also decided to check on what solutions were available from other 9-letter words. Only 20 9-letter words can form 3x3 magic word squares. Here is the list (omitting the mirror images of each square):

arterials
alt
ria
ser

dromedary
mod
ear
dry

entourage [only 9-letter word making two 3x3 magic squares that are not mirror images of each other]
not
eau
erg

gee
oar
tun

eyeballed
bel
yea
eld

fireboats
abs
fie
tor

hortatory
hot
oar
try
[this solution is its own mirror image]

isophotes
ops
hoe
sit

laborites
abs
lie
tor

motorways
mos
oat
wry

naseberry
brr
yea
sen

pedaliers
ads
lie
per

playwears
paw
ear
sly

portrayer
rep
oar
try

seaworthy
hes
oat
wry

strobilae
abs
lie
tor

temporary
MET
OAR
PRY

throwaway
wot
aah
wry

waylayers
yaw
ear
sly

woodenest
ods
woe
net

woodnotes
ods
woo
net


I submitted these answers to Will Shortz:

<< Will,
I extended the current NPR listener challenge to look for all 9-letter words that can form 3x3 magic word squares. Here are the results. I plan to post them on my web page at: http://rrenner.home.igc.org/1929puzzler.htm

Here is Will shortz analysis of these possible answers:

To: rrenner@igc.org
Subject: Re: 1929 Puzzler Magazine solution for NPR puzzle
Date sent: Tue, 2 Dec 2003 10:07:37 EST

Hi Richard,

Thanks for the computer analysis of the 3x3 word square puzzle.

I think I lucked out, because the Puzzler version of this puzzle simply listed the nine letters in random order -- A, R, O, Y, R, P, E, T, M. I knew that NPR listeners driving to church, say, or lolling in bed on Sunday morning wouldn't be able to remember these if I read them like that, so I tried to anagram them into a word ... and voila, TEMPORARY!

This anagram seems especially fortunate, because I'd allow very few of your 20 other computer-generated solutions. In some the 9-letter words are obscure (ISOPHATES?), some have obscure 3-letter words (SER? ERN? ALT?), and at least one has a repeated word (DRY in DROMEDARY), which I'd consider a no-no.

Not many good ones left!

In case you're interested, the original puzzle appeared in the June 1929 Puzzler.

--Will


If you know any other thoughts on this puzzle, or you would like a copy of the program that found these solutions (after running from Sunday morning to Tuesday morning) please let me know.
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Richard Renner
New Philadelphia, Ohio
www.taterenner.com


Last Updated: 2003-12-06
NPR puzzle Copyright © 2003 by Will Shortz and NPR. Reprinted here with permission.