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Alphabetic latin square
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Bram



Joined: 04/03/2008 13:59:34
Messages: 359
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I've been trying to find for a while now a latin square with 4 letters where every line forms a word. I'm wondering if this feat is possible for 4 letters. Haven't been able to find one.

Some 3 word options where the fourth doesn't work.

E.g.:

Code:
 EMIT
 ITEM
 TIME
 METI


I found them with three letters.

Code:
 TEA
 EAT
 ATE


Last time I was trying to find something I was curious about (existence of unique 4 by 4 kakuro puzzles), Johan quickly found it out by writing a program (http://puzzlepicnic.com/puzzle?1754).
connect4


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Joined: 04/03/2008 05:04:39
Messages: 250
Location: USA
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Based on a program that I wrote using the 2of12inf list in 12dicts-5.0 (http://wordlist.sourceforge.net/), no such list exists.

The only triples are:

emit, item, mite
emit, item, time
ergo, goer, ogre
opts, post, stop
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Johan


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Joined: 22/12/2006 20:08:51
Messages: 1046
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Using the same word list I saw that the largest number of anagrams of 4 letter words is 6 (out of 24):
- east, eats, etas, sate, seat, teas
- opts, post, pots, spot, stop, tops

For 5 letter words we have 7 (out of 120):
-pares, parse, pears, rapes, reaps, spare, spear

For 6 letter words we also have 7 (out of 720):
- capers, crapes, pacers, parsec, recaps, scrape, spacer
- carets, caster, caters, crates, reacts, recast, traces

This is not a lot to work with and there is a lot of structure that gets in the way of making Latin squares, like words starting and ending with consonants mostly.

We can put 3 of the 5 letter words together without violating any latin square constraints:
Code:
 ..srp
 ..pea
 spear
 reaps
 parse
 
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