Castawords -- some thematic variant logic puzzles by Michael Keller

Castawords is a logic puzzle which appeared 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 WGR and various other 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