You are presented with a grid containing circles, in seemingly random positions. You fill in the lines of the grid to form an island, or galaxy around each circle. The galaxy shapes must be rotationally (or 180° or two-fold) symmetric around each circle, like the shapes shown here. They resemble little spiral galaxies, hence the name of the puzzle. When the puzzle is finished, the space is completely filled with galaxies, and every galaxy shape is symmetric. You have wrought order out of chaos!

In Japan, Galaxies puzzles are known as Tentai Show, which has an interesting double meaning. It means both “astronomical show” and “two-fold rotational symmetry”.

Nifty, eh?

I have carefully ordered these puzzles so that they get significantly harder as the book numbers get higher. You’ll also find that the larger (21×21) puzzles are a great deal harder than the smaller (7×7) puzzles. I suggest you start with the smaller, easier puzzles and work your way up.


Galaxy Puzzles

Eighty-seven year old puzzle constructor Yochanan wrote to tell me he has posted scans of his hand-made crossfigure puzzles. You’ll find 80 puzzles, divided into 4 collections here. I find these puzzles to be excellent. However, because they are scans from a book, it helps to zoom in on each page to make the puzzles legible.

Yochanan has donated these puzzles to my collection, and I intend to transcribe them into a digital format and produce a new set of clean & legible PDFs from them, when I get some free time. If you’re interested in helping out by testing the transcribed puzzles, let me know!

Yochanan’s Crossfigure Puzzles

UPDATE

I’ve transcribed the collection! If you’d like to help out by solving one (or more) of these and checking for mistakes, send me a note and I’ll assign you a range. Thanks!

Draft for transcribed puzzles 1-20
Draft for transcribed puzzles 21-40
Draft for transcribed puzzles 41-60
Draft for transcribed puzzles 61-80

UPDATE

The puzzles have been proof-read, and you can find them here. A big THANK YOU to puzzle solvers Blaine, Janet, Ed, Clark and Paul for helping out!

Dear Mr. Bumgardner,

I am President of Nextoy, LLC and KenKen, LLC, which owns
and controls all rights in the KenKen® and Kendoku® brands
of mathematical logic puzzles. I have recently learned that
you are publishing puzzles under the name KENNIE, which
is an infringement on our registered KenKen® trademark.

KenKen® is a coined term and is thus an inherently
distinctive, strong trademark when used in connection with
Nextoy’s mathematical puzzle games. Your use of the name
KENNIE in the title of your puzzles constitutes passing off
and falsely implies that your puzzles originate from Nextoy or
are otherwise approved, sponsored or endorsed by Nextoy,
the makers of the genuine ‘KENKEN’ puzzles. Accordingly, I
must insist that you immediately cease and desist from all
uses of the designation KENNIE or other use of our distinctive
“KEN” term, and from the manufacture, sale, distribution or
further use of any puzzles or other materials that infringe
Nextoy’s rights.

I trust that your infringement of Nextoy’s rights was
unintentional but as I am sure you can appreciate, the KenKen®
brand is a valuable asset and we must be diligent in ensuring
that our intellectual property rights are protected and maintained.
If your infringement of Nextoy¹s KenKen® brand was indeed
unintentional, your cooperation in immediately ceasing all
infringing activities and complying with the other terms of this
demand will be a significant factor in determining how far
Nextoy decides to press this matter, including its decision to
seek monetary damages, lost profits, equitable remedies, and
other relief as may be proper under the circumstances.

I look forward to your cooperation in remedying this situation
in the most amicable manner possible. If you have any
questions concerning the foregoing, please do not hesitate to
contact me. I look forward to your positive response.

Sincerely,
Robert Fuhrer
KenKen Puzzle, LLC (subsidiary of Nextoy, LLC)
39 Washington Ave.
Pleasantville, NY 10570

So… I am henceforth renaming my Kennies to Inkies.

Enjoy the Inkies!

I’m publishing a new kind of puzzle called a Kennie. It’s similar to a KenKen, but has a few minor differences. Kinda like those chocolaty sandwich cookies that aren’t exactly like an Oreo… Kennie puzzles don’t include those cheap freebie squares that make the puzzle easier to get started. Personally I prefer ‘em that way, since it makes the puzzle more satisfying to solve. Your opinion may differ.

Unlike the Times, I’m not stingy: Here are literally thousands of Kennie puzzles, for you to print and enjoy.

Happy solving!

You can download the resulting list, which contains over a million words, here. Each line shows how many books each word appears in. A second list, which shows how many times each word occurs in total, can be downloaded here.

I prefer the list that shows the number of books each word appears in. It has the effect of pushing down words which appear a lot in only a small number of books, such as the names of fictional characters.

I compiled these lists because I wanted to make some word puzzles. There are lot of free lexicons, or word lists out there, such as the ENABLE lexicon which is commonly used for scrabble-like games. However, for the purposes of making crosswords, word searches, and other puzzles, it’s very helpful to restrict the words to more commonly used ones, and to know how common each word is.

The popularity number of the word correlates well with how ‘juicy’ the word is, or appropriate for a word puzzle. For example, using my book count list, words at the very top of the list are quite boring structure words.

18374 by
18054 and
18023 the
17994 of
17963 a
17955 to
17946 in
17916 from
17912 with
17909 for

As we head towards 10,000, we encounter most of the common bread and butter words. These are also kind of boring.

15095 case
15094 none
15091 taking
15070 seem
15060 able

10776 buried
10771 report
10767 asking
10767 clean
10764 occurred

As we head from 10,000 to 200, the words get increasingly more interesting.

9781 plainly
9781 flat
9779 proofreading
9777 passion
9775 approaching
.
.
.
5999 commanding
5998 channel
5997 translated
5996 metal
5996 sixth
.
.
.
1999 conflicts
1999 spider
1999 bleed
1999 discrimination
1998 lends
.
.
.
599 studs
599 niggardly
599 symbolized
599 engraven
599 palliate

There is a sweet spot with a lot of very juicy, but still familiar words in the 300s. If I were selecting words for puzzle construction, this is the area I would favor. After the 300s, the words start to get increasingly more obscure.

359 pajamas
359 dressings
359 thievish
359 anatomist
359 ticks
.
.
.
200 darkish
200 acclimated
200 unfriendliness
200 moveth
200 undiscoverable

At the 200 mark, we’ve only covered about 38,000 words. There are 1,236,759 words in the list total, so we are are still at the top of a very long tail! Below 200, words get increasingly obscure, archaic, misspelled and foreign. We also hit a lot of proper nouns. Still there are a few legit, but rarely used words mixed in.

99 tingeing
99 marshmallows
99 somethings
99 feelest
99 petrify
.
.
.
50 anim
50 makeweight
50 godard
50 seraglios
50 vun
.
.
.
25 admiralties
25 vanni
25 senescent
25 futrelle
25 erechtheum
.
.
.
10 foretime
10 chargee
10 cabinetmaking
10 pneumonias
10 olivo
.
.
.
5 guisers
5 hairing
5 hipless
5 turms
5 arpasia
.
.
.
1 raskolink
1 baetan
1 succories
1 denudement
1 trotudas

UPDATE, March 23rd:

I measured the average book-count of the words in all the New York Times crossword puzzles since 1997 (their online archive goes back to about 1996). For each puzzle, I averaged the book-counts of the words that appear in my list (typically, about 80%-90% of the words in each puzzle). For most years, the average book-count falls between 2,008 and 2,180, and from year to year, the results can be surprisingly consistent.

Here are my averages:

1997 2070.93
1998 2154.20
1999 2113.24
2000 2180.20
2001 2131.94
2002 2141.65
2003 2115.29
2004 2114.60
2005 2034.01
2006 2026.20
2007 2035.31
2008 2033.90
2009 2008.76

There appears to be a marked shift towards more obscure words from 2004 – 2005.

Interestingly, there are only about a thousand words that fall in that NYT-Crossword sweet spot. Here they are:

pondering squarely pregnant paws scold cordiality cooler venturing variance hypothesis forefinger economic untimely dubious shepherds secular minimum pallor degrading fastidious desertion foretold heath discourage wintry wrenched peas raiment pensive reproof ankle flattened moore fisherman peninsula beholding identification wheeling maine unhappiness richmond frantically enhanced gorge extremities joyously stronghold hissed nut bowels repressed lending feasts cavern unfold memoirs onto invade ark structures forbids liver correctness abashed stumble clerical orchestra terrifying enchantment incomparable collapsed paler ballad recalls slack restraining motley rippling circled ardor lambs flapping shrug prettily avarice aforesaid educate glorified acquiescence acquitted dungeon blasted objective persuading fray forts statistics gathers levelled moderately splashed mirrors infected vacancy furs mates grating precipitate confiding ton grazing dispositions partnership momentarily framework attorney regulating fathom nimble ravages surpassing quieted hitting sustaining practiced darkening walled withdrawal unawares exceptionally howard fiend queens horseman dictates quarry waged coral pleasanter badge assurances subsistence italians manned alphabet bower reposed preachers variously anticipating arabian melodious slate hourly bled dejected dreamt discordant stormed purchasing sap unreal parlour dam couples humblest postpone butterflies chaps yells paw freeze forfeit eclipse advertisements dozens quitting romances uphold drunkenness agonies guinea forge tearful twig dispatched windy tidy bitterest dogged wastes disconcerted irritable tunnel contentedly backing uniforms gunpowder mineral pigeons repel pail territories ransom stab draped redemption individually medicines azure bony scissors ma invariable supplement repulsed entreaty capitals forbearance adviser unavoidable raining enlighten holiness countenances untold coil mutilated dancers thankfulness buzzing armor spoiling narrower adhere ardently undergoing indomitable devoting friction thrive ravine diverse floats hazy twain aspire visage quarrelling womanly shields initiative disappointments elaborately civility disobedience splashing festivities disasters bustling vicissitudes monopoly helen raid marshes fitful consigned illustrates apprehensive conscientiously fabulous colleagues profited wharf grievances countryman laurels diversity monastery target pounded conspicuously myriads hostilities atrocious vase overturned redoubled mountainous swallowing layer adherents sparing parchment trampling imaginations laughingly fictitious jet widows picnic prospective valour absorb yankee chocolate courtiers canoe chasm biscuit stairway jars adjustment ancestral roving catholics psychological milder adapt woollen loathsome rowing barracks signing banker grunted slumbers garret midsummer ignoble savings substantially resuming fostered mane prophesied forfeited swan loosed fortifications gloriously vouchsafed oratory jovial crescent stinging stamps commissions lanterns caresses merest universities insurance draughts surmise rebuked valid barbarians revolted humbled emerald contradicted halfway marvels excel nervousness pier stall illustrating grades surly utensils chagrin colouring murders northwest widening pitiable keener kent devilish conventions carving studded mat dwarf weights youngster compels resounded dispatch fried completeness dismissal undecided aiding dimmed plied illumined extensively needing graphic embroidery glimmering sash sauntered sniffed grasses pitcher rapt unerring offences exiled sucked raced fig streaks halo religions rhetoric advising fraught canadian hampered riders profile incur excellency benediction gregory particles diminutive chemistry infants lounging knocks elated mien propped reverent antagonism wade exhaust unduly needy girlish hoarsely mortified hercules initials scar flowery reproduction absorption excelled stains facilitate modify slap grounded wig lavished magnified agility hugh sponge irishman cultivating stalked fumes metals arena augmented enjoined fibre flushing biscuits attends nick soaring follower boom surest rhine proclaiming snatching paramount alluring clambered loom poultry intoxication slaughtered perplexing impaired sleek patting conceited squirrel inventor notably swells ripened click ethics fairies adventurer summoning vocal jove scolded dwellers uniformity sarah prairie capacities unfriendly uttermost hens gear penance unbearable sewed legion disposing mistook prestige organic unparalleled invaders laboriously trench steeped distraction dipping groped slackened beak salutary summits intrusted inanimate flowering reiterated receding jagged adversity safeguard unacquainted stalks axes alps hip mortality perverse apathy weighs julius witnessing epithet childlike lunatic pretends convict oblivious restlessly yarn offense chests runaway dilapidated unfailing verdure cloudless ferry vista toll prettier unearthly enlist feudal penitent scarf encamped dedication mahogany relinquish residents salmon payments meditations tragedies sufferers concludes arnold smoky altars squadron pursuers sagacious abnormal bernard reeled strangled cherry planets combatants bunches feathered fearlessly therefrom canst precipitated likelihood potato conquests intensified columbus hairy slapped scrupulously immemorial buoyant graver warranted senator excesses invading complimentary turks highness factors vindictive shovel tenderest uncanny augustus propositions detection efficacy artful iniquity emancipation listless indolence lease purified grease unoccupied encounters treasurer hereby narrated revel impetus legislative wailed mexican disappoint impertinence abstraction pulls submissive surged falsely sheriff wilder underwent submitting prisons implicitly treasured sculpture spheres trailed impassioned exacted converts pepper coloring noiseless conflagration relatively maddened precincts versed quartered culprit tunes torments birch fairness unsteady terminate offender citadel ado compiled

The Griddle is a beautifully designed puzzle site by David Millar. It will especially appeal to more advanced solvers who are bored with the same-old same-old.
You’ll find a new puzzle variety, in PDF format, nearly every day, including some interesting variants on Sudoku, Kakuro and Slitherlink.

Check it out!

These numeric crosswords are similar to Kakuro and KenKen puzzles, but have greater variety in the clues. Here’s two to start with. I hope to post Yochanan’s complete set at a later date.

Crossfigure Puzzle #35 (pdf)
Crossfigure Puzzle #39 (pdf)

Wired is one of many magazines that has been noticeably suffering from the downturn in the publishing industry, and I had allowed my subscription to lapse a few months ago. This issue, which was guest-edited by J. J. Abrahms, is full of fun little puzzles, and articles about mysterious things, such as the Georgia Guidestones. Even the logo font on the cover has been improved for this issue (I wish they’d keep it!).

Apparently, the puzzles in this issue go a little deeper than they appear on the surface. I imagine the puzzle solvers who visit this website (even those who are not regular Wired readers) will enjoy this issue as well. Check it out!

On a related note, I recently picked up 23 volumes of the Time-Life series, Mysteries of the Unknown, on Ebay, for a song (about a dollar a book). The production values in those old Time-Life books was remarkable, especially when contrasted with the shape the publishing industry is in today.

Enjoy!

All the heavy black areas were knocked off of my Kakuro puzzles. While they are slightly less attractive, I’m told they use up considerably less ink and toner this way, so I guess I’ll keep ‘em. I hope you like the new look.

Meanwhile, I’ll have to figure out something to do with all these odd shaped black pieces I have left over…

Tangram puzzles, anyone?