Castawords -- some thematic variant logic puzzles by Michael Keller

Castawords is a logic puzzle which appears frequently in the British puzzle magazine Tough Puzzles, and also (under various names) in U.S. puzzle magazines
(e.g. Dell Logic Puzzles, where it appears regularly under the name Dicey Words).  I have found absolutely nothing on the Internet regarding this puzzle, so I am collecting here some general information on the puzzle, some methods of solution, and a number of problems I have published in various places.    Unfortunately I have no idea who invented the original idea.

Imagine that the sides of four dice (cubes) are labeled with 24 different letters of the alphabet, and the dice are rolled a number of times to produce a dozen or so four-letter words (reading the topmost letter from each cube and arranging them in an appropriate order). For example, if the four cubes are labeled ABCDEF/GHIJKL/MNOPQR/STUVWX, some possible words are LURE, SOLE, and VAIN. The object of the puzzle, given a list of words, is to deduce the distribution of the 24 letters among the four cubes, based on the fact that each word contains one letter from each cube (and hence letters appearing in the same word cannot appear on the same cube).  When a puzzle is properly constructed, all 24 letters are present, and there is a unique solution.

(1) BACK BIRD CUTE DOWN FIGS FLUX JERK MANE MYTH PLOY SODA ZIPS

Let's try solving problem 1 above. We start by comparing SODA with DOWN, and see that S and A must combine with W and N in some order. But N cannot go with A because of MANE, so we have D/O/AW/SN. Next, M and E  (from MANE) must combine with D and O in some order : D(ME)/O(ME)/AW/NS. 
Consider the words BACK and BIRD; B cannot go with A or D. If B combines with SN, then C and K must go with D and O in some order -- but this is impossible, since either the D or O group must include E, which can combine with neither C (CUTE) nor K (JERK). So B must combine with O, and since C or K must combine with D, the D group must include M (not E).   So far we have: DM(CK)/BEO/AW/NS(CK). Now add I and R from BIRD. I cannot go with S (FIGS), so I goes with A and R with N. This forces C to go with N and K with D (JERK), and we can add the J to A. Next we add U and T from CUTE (T cannot go with M), H and Y from MYTH (Y cannot go with O), and P and L from PLOY (L cannot go with U). At this point we have: DKMPU/BEHO/AIJLTW/CNRSY. Only four letters remain. Look at FIGS and FLUX; F goes with B, X with C, and G with D. Finally Z from ZIPS goes
with B and we have the solution.

(2) BALE BASK COVE CURD EXIT FARM MOWS PAIN PITH TEMP UGLY ZANY

A more complex, but very powerful, method is to determine the six letters of each cube one by one, starting with one of the letters of highest frequency. In problem 2, we start with the letter A, and try to find the five letters which go with it. List the letters of each word not containing A as possibilities, each group in parentheses: A(COVE)(CURD)(EXIT)(MOWS)(PITH)(TEMP)(UGLY). Now remove each letter found in words containing A (i.e., LESRMPIY). We get: A(COV)(CUD)(XT)(OW)(TH)(T)(UG). Since T is the only possibility from TEMP, we add it to A, outside the parentheses, and eliminate H and X. Now we have only four words left (not containing A or T), and each must provide a different letter. Thus we can eliminate the repeated letters O, C, and U. This produces ADGTVW as the only possibility for the cube containing A. Now follow the same procedure with another high-frequency letter not already placed -- let's try E, eliminating all other letters in words containing E, as well as the established letters ADGTVW. We get E(SK)(UR)(FR)(S)(N)(H)(UY)(ZNY), and can immediately add HNS to E, eliminating K, Y, and Z. This also leaves us U, eliminates R, and adds F, yielding EFHNSU. Neither of the first two dice contain M, so we can reconstruct a third cube starting with M. We get M(BL)(BK)(C)(XI)(I)(LY)(ZY), leading to CIM(BL)(BK)(LY)(ZY). If Y is right, L is wrong and B is right, giving
us only five letters. So Y must be wrong and L right, giving us CIKLMZ.   The fourth cube can be found by listing the unused letters from each word (BOPRXY), completing the solution.

Here are some more standard problems to try. All of the puzzles here have twelve words or fewer; problems 13-15 (which appeared in 1992) may have been the first published constructions with 11 words.    To my knowledge a 10 word example has never been composed, nor proven impossible.   Note that (5) contains all colors -- the first thematic I ever constructed; (7) omits the two most common English letters E and T; (16) is a later thematic example using birds (a bit on the obscure side -- these are brutally hard to construct):

(3) BOAT CHAT DUNE FLIP GRAD NOSY PEAK QUIZ TRIM VEIL WHIP ZEST
(4) AXIS CRAG HALF JAMB JUTE KEYS MOLD PATH PING SHOT VENT WIRY
(5) BLUE FAWN FLAX GOLD GRAY JADE NAVY PINK PLUM RUST TALC ZINC
(6) CURB DAMP HARD JEST LONG LYNX MOCK QUAY TEAR VANS WHEY ZEBU
(7) BORN CALM DOCK FILM GRIM HAZY JAWS JINX PUSH QUID VARY YANK
(8) BECK BOND CHEF EXAM MUTE PURL QUIP THEY TOGS VISA WAIL WREN
(9) BRAY DUST FLOP GLUE HINT JIBE MAZE NAIL QOPH VIOL WARM XYST
(10) ARMY BUNT CORE DOZE FLOW GIFT JAIL MANX QUAD RISK SIGH WIDE
(11) BUSY CHEW DING FIVE FOUR JEST PIGS SWAN TANK WHOM XRAY ZERO
(12) AXLE BONY DAYS DUCT DUNK FARM JUMP POSH RAZE SCOW THUG VOLE
(13) BOWL CLIP DARK FEUD GNAT HUMP JUNK JURY MIST OXEN WAVY
(14) DIKE FROG GLIB HUNT JOKE LADY PRIM QUIT SUCH SWAM VINE
(15) BAND CENT CLOG EXPO HIVE HONK MELD QUAG SIZE SPRY TURF
(16) APUS CHAT COLY DOVE FINK GUAN JYNX LARK STIB TODY WHIM XEMA

A Red Herring

Twelve of the words below are normal, but one word is a red herring, consisting of four letters from the same group of six. Find which word it is and solve the puzzle. (Hint: If a pair of words have two letters in common, neither can be the red herring. For each possible red herring, try to find the two companion letters).

BURY FACT GAZE GILD HAND HATE HYMN JOIN MARK NECK PLUS VOTE WEST

More complex versions of Castawords

The idea of extending to five letter words was suggested by Eduard Riekstins, who at the time edited a puzzle column in the Latvian newspaper CM Cevodnya.  He published several Castawords puzzles (in Latvian) in his column; he sent the following English one to me, which obviously inspired one of my puzzles below:

A puzzle-lover has found in his attic five toy letter-blocks from his childhood. Each block contains six letters. With these cubes he can produce the following words (mostly related to games):

BLACK BOARD CHESS CRAZE FACET JOKER LOTTO NORTH PAWNS POINT
POKER QUEEN SEVEN SHOGI SIXTY TRUMP VIXEN WHIST WHITE

Here are some more of my thematic puzzles, which appeared in 2000 in the now-defunct website The Games Cafe.  

Game Logic

You have five blocks with letters of the alphabet on (most of) their six sides.  Four of the five blocks contain five different letters and one blank side; the fifth block has six different letters. No letter is repeated, so each of the 26 letters appears exactly once.  By arranging and turning the blocks, you can spell each of the 14 words below, which are all names of games.   Words shorter than five letters must use blank sides, so that HEX requires that H, E, and X be on three differennt blocks, one of which contains six letters.   Can you deduce what letters are on each block?

Some of the games above may be unfamiliar:
Clue (a detective game), Junta (a political game), Probe (a word game), Qubic (4x4x4 tic-tac-toe), Realm (an abstract board game), and Risk (a multiplayer war game) are commercial board games.   Hex is another abstract board game, as is Oware, a form of mancala.   Ghost is another word game.  Durak is a Russian card game, while Vira is a card game from Sweden.   Frog, Giza, and Yukon are types of card solitaire. 

 CLUE
DURAK
 FROG
GHOST
 GIZA
  HEX
JUNTA
OWARE
PROBE
QUBIC
REALM
 RISK
 VIRA
YUKON

Animal Logic

This time you have five blocks with letters of the alphabet on all of their six sides.  Four of the 26 letters are found on two different blocks each, so that there are 30 letters in all -- unlike the previous puzzle, there are no blank sides. By arranging and turning the blocks, you can spell each of the 17 words below, which are all names of animals.   Can you deduce what letters are on each block?

APHID
BISON
CHIRO
CIVET
COYPU
FINCH
HYRAX
JUREL
LLAMA
MOOSE
OKAPI
QUAIL
SHEEP
SHREW
SQUID
TIGER
ZEBRA

Musical Logic

Dmitri Plekharanov's Lyric Suite is famous for its variety of dances, including a polka and a waltz. The major sixth chord in the opening movement is followed by a clarinet motif that emphasizes the break between registers. The second movement consists of a round, each voice playing the same melody twice.



Put 25 letters onto five blocks (each having one side vacant), so that each five-letter word in this puzzle can be spelled with one letter from each.

Castawords as a two-player deductive game

I introduced into NOST (the Knights of the Square Table, a now-defunct postal club for chess, chess variants, and other games) a two-player version of Castawords. Each player selects a Castawords grid (four rows of six letters). Players then alternate guesses (four-letter words with no repeated letters). Each word is scored according to the distribution of its letters in the opponent's grid : a score of 1 1 1 1 indicates that each row contains one letter, 2 1 1 (the most common score) indicates that some row contains two letters and two others contain one each, etc. (Words containing one or both missing letters can receive scores 1 1 1, 2 1, 3, 2, or 1 1). A sample grid and examples of each score :

CANE CHIP DOGS FARE FLOP GNAT GRIM
JAMB JOKE LOCK MAIN MAST MINK NOSE
OKAY PICK QUIZ SAME SAND SITE STAY
STEM SOUR SWAM TAKE TAME WENT WHOM

Portions of this article previously appeared on the Games Cafe (www.gamescafe.com) in 2000; that site is no longer in operation.

This article is copyright © 1992, 2000, 2007 by Michael Keller.  All rights reserved.