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
or Building Blocks). Unfortunately I have no idea who
invented the original idea. I have found
virtually nothing on the Internet regarding this puzzle (you can find a couple of examples by searching for Dicey
Words 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 The Games Cafe. Solutions to all of the puzzles
(including detailed solutions to most of the harder ones) are on the solution page.
Imagine that the sides of four dice or wooden blocks (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. As we assign letters to the
various blocks, we will call each
block by the letters which we know are on it, in alphabetical order.
(1) BACK BIRD CUTE DOWN FIGS FLUX JERK
MANE MYTH PLOY SODA ZIPS
Let's try solving problem 1 above. We start by comparing DOWN with
SODA, 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 / NS. Next, M
and E (from MANE) must combine with D and O in some order: we'll write
this as Dme / Ome / AW / NS, the lower-case letters indicating
possibilities. Consider the words BACK and BIRD; B cannot go with
A or D. If B combines with NS, 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, which we already know cannot combine with
C or K). So far we have: DMck / BEO / AW / NSck. 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).
(17) 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 Lettish and Russian) in his column; he sent the following English one to me,
which I published in WGR12; it obviously inspired my puzzles Game
Logic and Animal Logic
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):
(18) 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 different 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. This puzzle is not
as hard as it looks.
(19)
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?
(20) APHID BISON CHIRO CIVET COYPU
FINCH HYRAX JUREL LLAMA MOOSE OKAPI QUAIL SHEEP SHREW SQUID TIGER ZEBRA
Musical Logic
(21) 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 Goes to the Movies
(22) ANTZ BLOW CARS DAVE FIST HELP HULK JAWS MASH RUDY TAXI TRON
Second feature
One or more blanks (which do not appear in the movie titles) can be on any of the five blocks.
(23) ALIEN BUGSY EVITA FARGO GILDA JANIS KLUTE MARCO MELBA PANIC PIQUE SHANE TOXIC WATER ZELIG
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 :
AHJLUV
HAUL
4 WIPE 3
BCIPWY CLIP 3
1 BATH 2 1
DGKNOX LOAN 2
2 STOP 1 1 1
FMQRSZ FLAP 2 1 1 TONE 2
(-et) BARK 1 1 1 1 DATE 1 1
Here is a problem based on the two-player version.
The following 28 words have been guessed for a certain grid; all 28
give the result 2 1
1 -- what is the grid?
(24)
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
Much of this article, including puzzles 1-15 and 17, originally
appeared in WGR11 (June 1992, pp. 23-24). Puzzles 19-21 previously
appeared on the Games Cafe (www.gamescafe.com) in 2000; that site is no
longer in operation (an unrelated game site now occupies that domain
name). Puzzles 18 and 23 originally appeared in WGR12 (January 1994,
page 4). Puzzle 16 appeared in WGR13 (February 1998, page 14). Puzzle 22 was newly composed (September 18, 2011) for this page.
Two of my other thematics were published in Dell Logic Puzzles
(December 1995, page 19; August 1996, page 37).
Most recently edited on September 23, 2011. This article is copyright © 1992, 1994, 2000, 2007, 2009, 2011 by Michael Keller. All rights reserved.