How to begin? For lack of a better description, Planetarium is a story-puzzle in twelve weekly installments, into which is woven a fantastical fable and many marvelous puzzles. Beholder, the British developer of Planetarium, has concocted an intriguing tale: a young girl, with no memory but perfect foresight, receives a love letter from far into the future. Together with her friend the Mathemagician, a genius with an aptitude for machinery and mathematics, she must travel towards the source of that strange missive, and in doing so, undergo a transformation that will alter her very essence.

Beginning the game is easy. Simply create a username and password, and you're set—you're not even required to submit an email address (By the way, did I mention that no ads appear anywhere on the game's website? I love it!). The moment that you register, the game has begun for you, although there is a slight catch. The ruling force in Planetarium is Time: the vagaries of time, its mutability and stony inevitability. This theme suffuses Planetarium's story, its puzzles and, as a natural extension, its rules and restrictions.

Only the first chapter of the game is immediately playable. The next chapter will be available a week later, and the third one a week after that; all in all, that means that Planetarium fully unfolds over a three-month duration. This period begins the moment that you register a username, so every player is on his or her own individual timeframe.

Another important note: Planetarium requires you to log in (even for a moment) at least once every 10 days, or your username will be frozen. I am not the most patient person in the world, and I must admit that at times this slooooowness drove me to distraction. In the end, however, the protracted pace of the game made it all the more rewarding.

Each installment consists of an illustrated scene and a significant amount of accompanying text, depicting another step in the journey of the unnamed girl and the Mathemagician. Three puzzles can be found in each chapter, by clicking on the appropriate hotspots in the illustration: a keyword puzzle (mainly riddles), a number problem, and a tricky "either-or" question. Cumulatively, these 36 problems are the game's Minor Puzzles; each solution that you enter goes into a slot in your Table of Solutions.

36 puzzles… that's quite a daunting task. The creators of Planetarium could be forgiven for recycling classic puzzles, and indeed some of them (particularly the riddles) may be familiar to you; however, most are unique to the game. Many of these thoughtful, often elegant problems require abstract, out-of-the-box thinking; others require the player to hunt through past or future installments for information (which means that not all can be solved immediately). While most of the puzzles do not require outside information to solve, you'll find that Google will probably be needed for a handful. All in all, this collection of puzzles is a pretty remarkable achievement.

That being said, those 36 puzzles are not what make Planetarium so memorable. The Minor Puzzles, in fact, are only the stepping stones to unlocking Planetarium's heart, its true mystery: the Major Puzzle. Never explicitly described, the identity of the Major Puzzle must be detected through clues and hints embedded in every conceivable place in the story. It's up to you to discover how to solve the Major Puzzle; but as the game's website notes, if any of your Minor Puzzle answers are incorrect, your answer to the Major Puzzle will probably be wrong as well.

After twelve weeks, you'll be granted access to the complete, illustrated solutions to both the Major and Minor Puzzles (thank goodness!), as well as the "xiii forum", where players can share their thoughts on the experience. But even this is ruled by time; one week after you gain access to the forum and solutions, your username expires and you may no longer see past the first chapter of the game. If you want to venture further, you must create a new account and once more endure the long weeks between installments. There's something poignant about knowing that your time in this game is ending, that its secrets will be closed off once more; even after the curtain falls, the ticking of the clock never ceases.

I could go on for quite a while. I could talk about the cleverness of the game's prose, the quirky beauty of the illustrations; I could expound upon the intricacies of the game's themes and the elegance of the clues. But why drone on about what you can discover for yourself? Planetarium is the best kind of entertainment in its purest, most unblemished form; it exists entirely for the enjoyment of its players, and has done so since 1999.

Create a username and password, and off you go on your twelve-week journey of whimsy and erudition. Don't be surprised if this brilliant, unique and beautiful game soon becomes one of your favorites.

## Walkthrough Guide

(Please allow page to fully load for spoiler tags to be functional.)

Here's the walkthrough. I put puzzles in the part we encounter them in the game, not in the part they go to in the Table of Solutions.

Special note to those who come to this game after we did: It might be worth taking a look through the comments to see the steady progress we made each week. I enjoyed the conversations immensely.

Minor Solutions:Part 1: (first posted by RacerX, with Framli for the Ouroborouses)

Keyword

Location

The mathemagician's riddle.

Clues

Each line has a word hidden in the first part.

Answer

These words are eight, one, seven, and nine. So the answer is NUMBER (always choose singular, never plural).

Keynumber

Location

Tripod, the Three-Legged Cat

Clues

A number whose length (in letters) matches its value, stride for stride.

Answer

4 is the only number that fits, and Tripod used to have four feet.

Either/Or

Location

The ouroboruses (snakes in jar behind the girl's head, to the right of the sun).

Clues

You'd think that they couldn't get caught and tangled, but is it intuitive, or counterintuitive?

Answer

Strange as it may sound, it is possible for them to get tangled up, even if all are wise. Look for "Borromean rings" on Wikipedia or mathworld.wolfram.org for more information. Once all of them have bit their tails, then they can all be kept in the same place.

Part 2: (first posted by JIGuest)

Keyword

Location

The vole (perched on the milestone) is puzzled. The puzzle is the location.

Clues

Rats can become their reflection, and so can a dog. And the rats could not escape the dog even if both were reflections.

Answer

I like this puzzle. "Rats" spelled backwards is STAR. And "Dog" then becomes "God". STAR is the answer.

Keynumber

Location

The number grid on the upper right.

Clues

Remember the previous grid. The cells in this grid have been exposed to the numbers in adjacent cells, but not their own.

Answer

Each cell in this grid is the sum of the cells adjacent to it in the previous grid. Example: the upper left corner in the first grid is adjacent to both 2 and 4, so the upper left corner in the second grid is 6. By the same reasoning, the bottom left corner has number 12.

Either/Or

Location

The milestone.

Clues

The milestones are identical, the shortest distance between the two houses is 1 mile, and the second milestone was never seen again after the dispute was honorably settled.

Answer

Consider a tetrahedron (a d4 or four-sided die for RPG nerds). All the points are equidistant, so if the houses and milestone in the picture make up three of the corners, the other milestone makes up the fourth. Of course, it can't be suspended almost a mile in the air....instead it's buried almost a mile underground. So the mathemagician had to pay, and I can't help but think that he was profoundly satisfied at the solution.

Part 3: (Luonnos for the Keyword, Sruixan for the Keynumber, and Wisedude for Either/Or)

Keyword

Location

The red grid to the upper right.

Clues

Lunar time is numbered in a particularly simple way. What if we just started numbering from the beginning?

Answer

L=1, U=2, etc. With the insertion of the P at the beginning and the a somewhere in the middle, then we get PLANETARIUM.

Keynumber

Location

The chemicals on top of the desk.

Clues

There are a series of numbers given, a formula not a sum, which answer is a 2-digit number. What associated with chemicals might have numbers?

Answer

Use the periodic table of elements to translate Atomic Numbers to Atomic Symbols. The resulting text is F I V Es I Xe S, or five sixes. The answer is 30.

Either/Or

Location

The orrery's 'interaction of all the precise parts'.

Clues

Look up 'Eulerian walk' or 'Eulerian path' on Wikipedia or mathworld.wolfram.org or look below.

Answer

In this section, 'vertex' will be used to refer to any of the 9 planets, three moons, or the sun. 'Edge' will be used to refer to a track connecting two of these objects.

We see that all of the planets are connected to four other planets. Note that this means that starting from any planet, you can reach any other planet. [Proof: Each planet is connected to four others, leaving only four that it is not connected to. Now each of those four planets has four tracks coming from it, so at least one of them must go to one of the planets that the first planet is connected to (since no track can go to itself or to the initial planet, and there are only three other planets that are not directly connected to the original planet). Since the choice of planet was arbitrary, all planets are reachable from any other planet.]

We see that all planets except Earth have 4 tracks.

We see that Earth has 6 (4 from planets, 1 from the sun, and 1 from the present moon).

We see that the sun has 4 (1 to each moon, and 1 to the earth).

We see that the present moon has 4 (1 to each of the other moons, 1 from earth, 1 from sun).

We see that the future and past moons both have 3 (1 to each of the other moons, 1 from the sun).

A well-known result from graph theory states that if a graph is connected (you can get from every vertex to every other vertex) and only two vertices have an odd number of edges, then it is possible to go from one of the vertices that has an odd number of edges to the other vertex that has an odd number of edges following a path that uses every edge once and only once. So it is possible.

Part 4: (Alkalannar for Keyword and Either/Or, Wisedude for Hydra)

Keyword

Location

The triskelion. (Three-legged beastie with the goofy face.)

Clues

Wow, sounds like this thing destroyed houses, dressed up like a woman, wears sheepskin, occurs either as lone or in a pack. These should be a dead giveaway. Personally I like the following:

Aconite is wolfsbane, and a backwards ebb is a flow.

Answer

WOLF, of course.

Keynumber

Location

The multi-headed hydra.

Clues

This is straightforward math: what number is left when you're done dividing 40 by 2 repeatedly?

Answer

Well, 5...but then you have to add 1 to get the head that never got chopped off. So 6.

Either/Or

Location

The crystal balls by the Triskelion.

Clues

The crystal is absolutely uniform, the crystal ball radii are in ratio of 1:2:3, and the volume of a sphere is [(4/3) * pi] (from here on out called X) times r^3, where r is the radius.

Answer

Let the radius of the present crystal ball be 1.

Since the original crystal orb contains both a ball of radius 2 and a ball of radius 3, the original orb must be at least radius 5.

The volume of a sphere of radius 5 is 125X.

The sum of volumes of spheres of radius 1, 2, and 3 is 1X + 8X + 27X = 36X

The amount of crystal shards left over from a radius 5 sphere after radius 1, 2, and 3 spheres are taken away is 125X - 36X = 89X.

So there will always be at least 89X in shards, where the three spheres together are only 36X. (If the orb has to be larger than radius 5 to get the three crystal balls out of it, then there are even more shards.)

So there is more in the bag than the combined three crystal balls.

Part 5: (Alkalannar for Keyword and Keynumber, muddgirl for Either/Or)

Keyword

Location

Moths around the lantern

Clues

"Not sun heavy", astronomical light reflected, influences those who are insane, enjoyed by lovers, scary beasts, and the brightness (albedo) is less than the original.

Answer

MOONLIGHT. Sun is opposite of moon, light is opposite of heavy. Reflected from the sun. Lunatics are mad and hairy. Lovers enjoy moonlit trysts, and werewolves change under the full moon.

Keynumber

Location

The map on the table between the lantern and the books.

Clues

Back in part one, look at the abacus. Simple math gives the radius of the city of Round as 6 miles. Also note in this week that there are four marks on the map that appear to be the corners of a rectangle.

Answer

In a rectangle, split the vertices into any two pairs. Then the lengths of the line segments connecting those pairs are equal, whether they are parallel sides or diagonals. Since the distance from the tall tower to the gate is 6 miles (as it's a radius of the city), then the distance between the two shorter towers is also 6 miles.

Either/Or

Location

Wooden box in the upper left.

Clues

Again, like the week 1 Either/Or, this seems like it's going to be either very intuitive or counterintuitive.

Answer

I got this one flat out wrong initially using logic. Instead, I was directed by muddgirl to google "dovetail puzzle". The pedlar's claims could be true.

Part 6: (Lavos for Keyword, Alkalannar for Keynumber, Luonnos for Either/Or)

Keyword

Location

The hummingbird on the pirate captain's shoulder.

Clues

This one is short, and I don't think I can give any clues save the actual answer. Sorry.

Answer

WINDOW. It fits all the lines of the riddle.

Keynumber

Location

The flags on the Quartermaster's ship

Clues

Look at Wikipedia for signal flags.

Answer

The blue flag with a white circle is a 2.

Either/Or

Location

The letter/number grid on the upper right.

Clues

This is an esoteric math puzzle. No real help I can give other than googling...

Answer

...the 36 officers puzzle. It turns out that every voyage has at least one person grumbling.

Part 7: (HenkSnow for Keyword, Wisedude for Keynumber, Alkalannar for Either/Or)

Keyword

Location

Yellow fishes.

Clues

First letter is in both 'grudge' and 'hater', second letter is in 'tyrant' but not 'traitor', third letter is in 'battle', end 'belongs to me'.

Answer

ENEMY

Keynumber

Location

Jellyfish....and those are tentacles, not legs!

Clues

Hmm...the branches of the tree back in week 2 look odd...

Answer

The spaces between the branches form the letters XIS. So look at it from the perspective of the mathemagician and the girl, and it reads SIX. (Actually, it reads ZIX, but close enough....)

Either/Or

Location

Shark

Clues

We can't answer this until week twelve. Until then, just count things that have an odd number of legs.

Answer

Week 1: Tripod

Week 4: Triskelion

Week 6: Quartermaster

And....that's it! So there are an odd number of legs.

Part 8: (Alkalannar for Keyword and Either/Or, Alkalannar with huge assist from Wisedude for Keynumber)

Keyword

Location

The man on stilts discusses what the astronomers are observing.

Clues

The sun, but not quite. Something in the way, but the thing in the way is not what they're looking for either.

Answer

ECLIPSE.

Keynumber

Location

The mathemagician.

Clues

The mathemagician is dreaming of the hydra we met back in the girl's dream (part 4). (Killing a nine-headed hydra was the second of Hercules's Twelve Labors.) The number was caught in the horns of a dilemma and the dilemma turned into the multi-headed hydra.

Answer

Looking back at part 4, we see that several of the hydra's heads have horns that bracket letters. Wisedude first pointed out the O. Specifically F, O, U, and R.

Either/Or

Location

The middle (second) astronomer.

Clues

The third astronomer cannot determine whether his monkey has a tail. Using that information, and the type of monkey that first astronomer has on his back, the second astronomer can determine his type of monkey.

Oh, and look back at the empty cage in week 6 to find out the number of monkeys with tails.

Answer

The first and second astronomers can't both have monkeys without tails, or the third astronomer would know that the monkey on his back had a tail. So there must be at least one monkey with a tail among the first two astronomers. If the monkey on the first astronomer's back had a tail, then the second could not figure out if his had a tail or not. So the monkey on the first astronomer's back has no tail, and the monkey on the second astronomer's back has a tail. [Note: Once the second astronomer announces that he knows what kind of monkey his is, the first astronomer can figure out what his is.]

Part 9: (DavidB for Keyword, Alkalannar for Keynumber and Either/Or)

Keyword

Location

Weathervane

Clues

Looks like a list of names in alphabetical order, alternating male and female, except there's Patty and Sandy. So it looks like we need a male name beginning with either Q or R. Where could I find a series of alternating alphabetical male and female names?

Well, "If only he could free himself from the bonds of ironmongery, he could leave his rooftop perch and pay a visit to the mathemagician's study, where there is a map of the time and place to which these names belong." And in the mathemagician's study (week 5), there is a map of the ocean labled "North Atlantic, 2000 A.D." (Thanks again for this tidbit, muddgirl!)

Answer

These are the names of hurricanes. The missing name in this list is RAFAEL.

Keynumber

Location

Lighthouse

Clues

Go back to the seahorse in week 7. The letters in the message are all Es, Is, Ss, and Hs, except for a single R.

Answer

E is ., I is .., S is …, and H is …. in Morse code, so none of them contribute any long flashes. The single R is .-., so there is 1 long flash in the seahorse's message.

Either/Or

Location

Potions at bottom left, or the second building on the left (not the one with the key banner).

Clues

Again, this is one of those puzzles where you either trust your intuition, or you don't.

Answer

Let the volume in each bottle be X.

Let the amount of red in the primarily red bottle be R1 and the amount of red in the primarily green bottle be R2. Similarly, let the amount of green in green be G1 and the amount of green in red be G2.

Now R1 + R2 must equal X (as the red bottle has X red liquid in it to begin with). G1 + G2 must also equal X. Now after the mixing, R1 + G2 must equal X (a spoonful of liquid was removed from red, then one was added back), as must G1 + R2 (spoonful added, then removed).

So R1 + R2 = R1 + G2 and R1 + R2 = G1 + R2. Or R2 = G2 and R1 = G1. So the amount of red in one bottle equals the amount of green in the other bottle.

Therefore, there is not more red in bottle than green in the other.

Part 10: (First posted by Alkalannar)

Keyword

Location

The Fox's riddle (the card in his hand).

Clues

Something that masquerades as asterisks. (Or did in 1999...some things have changed in computer display technology. Nowadays, they mainly masquerade as small filled-in circles.) And then examples are given.

Answer

PASSWORD.

Keynumber

Location

Dominoes

Clues

Straightforward math here: there are 7 dominoes that have a particular number on them (i.e. 7 with 0, 7 with 1, etc.).

Answer

But...one of those dominoes is a double, so there are 8 of each number from 0 to 6.

0 + 1 + 2 + 3 + 4 + 5 + 6 = 21. 8 * 21 = 168.

Either/Or

Location

The Game of Cards

Clues

We have 0 face up. We want 5 face up. We can only change 2 cards at a time.

Answer

It is not possible to win without cheating. A turn (flipping two cards) either:

a) flips two cards face up,

b) flips two cards face down, or

c)flips one card face up and one card face down.

In particular, if you start with an even number of face-up cards, then you will always have an even number of face-up cards, and never an odd number like 5.

So the wolf cannot beat the fox's score without cheating. On the other hand, the fox cheated to win in the first place, probably by using the card with the riddle on it that he's handing to the girl.

Part 11: (David B and Uncle Arthur for the Keyword, Alkalannar for the Keynumber and Either/Or)

Keyword

Location

Iguana, then 'animal kingdom'.

Clues

There's a mouse in the picture surrounded by the ghost! (The mouse's tail goes just under the ghost's jaw.) And apparently something like this happened back in week 2. So what animal (neither owl nor vole) is hidden somewhere in week 2 that shares three letters with mouse?

Answer

Underneath the milestone in week 2, there appears to be a shell, and beneath the ghost's foot a head. It's upside down though. Hmm...looks like a turtle, but turtle shares only 'e' with mouse. How about TORTOISE instead?

Keynumber

Location

Number grid on the upper right

Clues

These numbers are the product of the past. And this grid looks suspiciously similar to the ones from weeks 1 and 2.

Answer

Multiply the lower-right cells of the first two grids to get 9 * 14 = 126. Also note that the lower-left cell here is obscured so that you can't use this grid and week 1 to get the keynumber for the week 2 puzzle.

Either/Or

Location

Glass pieces below the number grid.

Clues

Letters in color * sides on base gives Odd or Even. (X denotes an empty space.) Ang thoughtfully calculated all of these for us.

Answer

The top layer (from part 4) is:

E E O

E O E

X E E

The middle layer (from part 7) is:

O O E

E O O

O E E

The bottom layer (from part 9) is:

E O O

O E E

X O O

So odds (the fox) won with top-upper-right, middle-middle-right, and bottom-lower-right. This is interesting since there are only 12 odd pieces and 13 evens. More cheating? Weird rules? The world may never know....

Part 12: (Wisedude and muddgirl for keyword, muddgirl for Keynumber and Either/Or)

Keyword

Location

The boy. (Or rather the construct that the mathemagician built.)

Clues

It looks as though you have to find an appropriate text, and look at the first letters of words that have double letters. These will in turn spell four words that give the clue to the real keyword. And in stanza 6, it appears that the text is from the disguise in part 9 that has so far been unused.

Answer

Getting the first letters of the double-letter words in the disguise description yields prunus avium prunus cerasus, which are two types of cherries: sweet and sour.

CHERRY

Keynumber

Location

The die.

Clues

Go back to part 10 and look at the dice. Also, note that the opposite sides of die faces add to 7.

Answer

There are 5 dice, four of which have opposite sides hidden (for a total of 28), and one of which has 1 on top (so 6 hidden on bottom). This gives a total of 34.

Either/Or

Location

The sliding puzzle.

Clues

Look at the Fox's and Wolf's sliders in parts 5 and 8.

Answer

The Fox has the real slider! This surprises me a bit, though on reflection, it really shouldn't

Table of Solutions:In the notation below, C is clockwise, and A is anticlockwise (instead of CC for counterclockwise so that both have a single letter). Also, I consistently list Keyword, Either/Or, Keynumber, unlike the real table which has 1-6 as Keynumber, Either/Or, Keyword. And I wish I had a fixed-width font to work with. Anyway, the completed Table of Solutions should look like this:

1: WINDOW A 12

2: WOLF A 4

3: TORTOISE A 2

4: NUMBER C 1

5: MOONLIGHT C 126

6: RAFAEL A 168

7: PASSWORD A 6

8: PLANETARIUM A 6

9: CHERRY C 4

10: ENEMY C 30

11: ECLIPSE A 6

12: STAR C 34

Tiebreaker:Clicking on the 'introduces' link in week 6 gets you to the tiebreaker. This has no bearing on anything now, since it was to break ties among the people who first played the game back in 1999. Simply choose a name that you think fits the girl the best. I made the ironic choice of Clio, the Muse of History.

Major Solution:Basics

If you click on any of the large orbs around the pictures, you'll notice that a group of letters is added to the major solution. Also, if you add a group from week 2 then week 1, it is not the same as if you had done the same orbs but week 1 then week 2.

It looks as though the Either/Or solution shows a direction to travel, which implies that either the Keynumber shows how many orbs to count and the Keyword somehow shows a starting point, or that the Keynumber somehow shows a starting point and the Keyword somehow determines how many to count.

Let's assume that the Keyword somehow shows a starting point, the Either/Or shows a direction, and the Keynumber tells how far to go.

Clues

There were several clues that led us to the solution:

In part 7, there are the two buoys labeled 'CARDINAL' and 'CLUE'. Commenter Ang found out that the markings on the CARDINAL buoy is North, and the CLUE buoy is East. North and East are, of course, two of the cardinal directions (the others being West and South).

In part 10, the harbormaster is said to be able to measure the wind to within one sixteenth of a full circle. And thank Commenter Sruixan for spotlighting that. Let's see, that would be the four cardinal directions (N, E, S, W), the ones in between (NE, SE, SW, NW), and then the ones in between those: (NNE, ENE, ESE, SSE, SSW, WSW, WNW, NNW).

Ang then noticed that each keyword has at least one and no more than three of the letters N, E, S, and W. And taking them in order yields a valid direction (like WNW from WINDOW).

I noticed (after seeing the Mathemagician sent backwards in time), that there was a chain of animals on a mission stretching from at least part 11 back to part 1. In part 7 at the description of the herrings states that the first part of the solution is the last half of the game, and the last part is in the first half. And in part 9, the girl's description has the following: "In her foresight, the remaining events dwindle to at best a couple more scenes, and the ambiguity of the girl's future is reduced to a prediction as certain as counting down from twelve to one."

Oh, and Commenter Wisedude notes the following in part 5's Atlas of the Undiscovered World: "...and a water-marked compass on each page with one unbreakable rule. North is ALWAYS up." (The possibility of a variable north was raised in the comments.)

Lastly in part 12, there is indeed an explicit compass rose giving directions down to 1/16th of a circle, and in the description of the machinery, it says, "Not least because it knows that the solution to that puzzle starts here, and passes through Planetarium, installment by installment, along the same route as the message which preceded it. It also knows that, in the end, it is here together with the girl, whereas in the beginning that was not the case."

Method

Extract the directional letters from each word.

Imagine the circle is a compass rose with north at the top, and find the direction derived from the keyword. Note: this will *NOT* be an orb!

Count the keynumber of orbs from the starting point in the direction of the either/or solution.

Do all of the above starting in week 12 and going back to week 1.

Solution

12: STAR

11: TATEN

10: DEN

9: DATS

8: TART

7: WHAT

6: ENDS

5: TO

4: GET

3: HERS

2: TARTS

1: APART

Or: Start at end. End at start. What ends together, starts apart.

Amusing thoughts:The letter from the future:

The letter is delivered by a series of animals from episode 11 to 1: iguana, ladybug, opossum, vulture, eel, yak, ostrich, unicorn, newt, owl, and weasel. The animals form the acronym: I LOVE YOU NOW, which is the text of the Love Letter.

The identity of the lover:

It is a mechanical boy made by the mathemagician!

Major solution:

Well, many of us were apart, but going through the game together, we certainly have ended together, in time and collaboration. I've had fun, I hope everyone else has as well.

Posted by: Alkalannar | May 22, 2009 5:27 PM