This cat-purr follows cat-purr 2: this time, we take Al-hiss through the nyan Chro-cat-ic cat-flap.

"Alice, the cyan door!" It was strange, but Phi somehow knew that this was the right choice. The moment Phi finished saying that she was in motion, leading Sigma right and towards the cyan door.

Alice reacted admirably swiftly, waiting only to wave Clover goodbye and direct her towards the magenta door before joining Phi and Sigma by the cyan door. The three of them piled through into the holding area behind the door and watched as the other players made their way to their respective doors.

With the choice made for them, the other six players fell into line. Dio, bearing a gleeful grin, grabbed Luna's elbow and dragged her towards the yellow door while Quark followed them stoically. Tenmyouji followed K and Clover through magenta door. The cyan door stayed open just long enough for Phi to confirm that everyone had made it inside their respective rooms; as it closed, Phi felt a profound sense of relief.

Alice sighed haughtily. "That was pretty decisive, Phi, but I'd have preferred it if you'd given us a bit more warning. Or if you'd chosen Option A, like everyone but Dio wanted."

Phi was about to respond, but Sigma got there first. "Would you have rathered we were stuck there arguing until the doors closed? Phi's… brusque, yeah, but I think she did the right thing."

Phi decided not to challenge that somewhat-qualified praise, and waited for them to be allowed onwards. Sensors whirled around the room, scanning the three people trapped inside. They watched the sensors rise for an agonising amount of time until finally they were bathed in a pale blue glow and the secondary door, bearing a holographic plaque reading 'Crew Quarters', opened.

They were released into a tight, gloomy corridor, with four doors leading off the corridor, two doors on each side, and another door at the far end. That last door was clearly marked as the most important; it was just as obviously barred to them at present, with a prominent mechanism to the right of it displaying 'LOCK' in obstinate digital letters just above a keyhole. Phi examined the other four doors instead. While the one immediately to the right of the entrance was locked, with a pair of handcuffs firmly attaching the handwheel to a railing beside the door, the other three doors were unlocked.

Alice started giving orders the moment she had taken stock of the situation. Phi figured she was used to getting her own way. "Three doors open, three of us. We should search one each, and then meet back here in a couple of minutes to share our findings. Sigma, you take that room," Alice commanded, pointing at the door to their immediate left, labelled '01', "Phi, you search that one," – pointing at the room diagonally opposite from Sigma, labelled '04' – "and I'll take room '02'."

Since Alice clearly wasn't going to take any argument, and it was a good plan in any case, they split up. Phi opened her door to find a cramped box of a room. Closer examination of one of the walls found a compartment from which a small bed – just a thin mattress, really – could be extracted. This was some sort of bedroom, but it was far too uncomfortable to be a guest bedroom; Phi guessed that it was used by a labourer, or some other blue-collar worker, who would probably have worked in the warehouse they had just left. As Phi dropped the mattress down into sleeping position, she noticed an outline of a person inscribed in chalk on the surface, and that the area where the left ankle of such a person would be was torn out of the fabric. This was clearly a clue, but without any other information to extrapolate from, Phi was stumped, and uninclined to waste time on it. She moved on.

Next to the bed was a small, glass-topped table protruding from the wall. Phi noticed a small piece of metal glistening at her from atop the surface of the glass; Phi picked it up and ran her finger along it, pricking the tip of her finger on what seemed to be a tiny key head. Unfortunately, this key didn't have a handle, so it would be impossible to turn if it was placed in a lock. Phi noticed that the transparent surface of the table let her see into a tray located in a thin compartment just below the surface, but there was nothing in there. Above the table was a grating in the wall through to an unlit area between the rooms. Strangely, rather than being a full grid of holes, there was instead a pattern of holes and solid wall, similar to a bar code. Phi made a note of this then moved on.

Opposite the table was a cabinet. The lock on it was rather unusual. There was a number pad with nine buttons in a square above it, but rather than each button being labelled with a different number, each button instead had a '+' on it, while each column and row was headed by a number: '1', '2' and '3' for the rows, and '0', '3' and '6' for the columns. Assuming the each button put in the number that was the sum of the row and the column, that meant that the nine buttons acted just like a normal number grid. Phi decided to make a note of that. Zero: is fully prepared to obfuscate the controls of something just to waste time.

To the left of the cabinet was a poster. The parts of the poster that Phi could see depicted a woman standing by the seaside, but most of it was obscured by a thin layer of silver. When Phi scratched it with her fingernail some of the silver came off, just like on a scratch card, but not enough of it to justify trying to scratch it off now. She would need a coin or some other implement to scratch it away fast enough.

Finally, to the left of the poster was a telephone. Though she didn't expect it to work, Phi picked up the handset and dialled '911'. It didn't connect. Then Phi tried the numbers of some of her associates in Las Vegas. They also didn't work. Phi sighed, but though she was disappointed she wasn't particularly surprised. It would be insane for Zero to kidnap them and then give them a way to contact the outside world. These phones had been disconnected, or at least restricted to internal calls.

With the room completely searched, Phi rejoined Sigma and Alice in the corridor. All three of their rooms were similar: a bed folding out of the wall with a silhouette of a man and a piece ripped out, a desk with a sliding tray underneath, a locked cabinet and a phone incapable of making outside calls. The three of them compared the items they had found. When Phi held out the head of a key she found, Alice's eyes locked on it curiously.

"Wait, what's that? Hold it out again so I can look at it more closely," she said imperiously.

As Phi presented the metal cylinder again, Alice plucked it from her hand. Before Phi could react, Alice revealed a similarly shaped piece of metal, this time with three interlocking circles at the end. Alice compared them intensely. Eventually, she slotted them together, and Phi saw that Alice had made a full key out of the two parts.

"Okay, that's what Phi and I found," Alice said, "What did you find, Sigma?"

Sigma didn't respond. Phi saw that he was clutching a book to his chest, and shivering gently but excitedly as he held it even tighter. A tortuous and manic grin gradually distorted his face. Just as Phi became convinced that his smile was about to explode off his face, Sigma started giggling.

"I'm sorry… I ca't hold it in for a meowment longer…" Then Sigma burst forth with a colourful, pun-laden spiel, "I was trying to seek a way meowt through room one when I meownd this purrecious book about 'Schrodinger's Cat'. The purrfect litter cat pictures on the front were so cu-at that I was kitten with them instantly. But when I clawed it o-paw-n it wasn't meowt cats at all! It was just all science and catemathics. That was so infelicitous of it!"

Alice and Phi glanced at each other.

"I don't suppose you'd know how to translate that?" Alice asked.

"Nope."

Sigma catinued – oh god, now she'd started – but he seemed close to burning himself out. "I'm sorry. I de-claw-re, I'm not doing this on purr-puss. It's not catagious at all. Whenever I see a cat I start feline twitchy and I just have to say something k-witty!"

Phi sighed. "That wasn't witty. That wasn't even 'k-witty'. That was inane."

Alice held onto Sigma's elbow and manoeuvred him back to the room he had searched. "Maybe it's for the best if you put that book down now, Sigma. Actually, I don't think it will play any part in the puzzle. Well, if it does, one of us – someone other than you – can pick it up instead so this doesn't happen again." Alice seemed completely confident in her ability to manage her ridiculously hyperactive teammate.

Sigma let himself be led away. "I can leave it on top the safe," he said mournfully. Then he perked up. "Oh, wait! That was in there as well. There was a safe like the one that had the key that let us out of the elevator. I think we need to unlock it to get out of here."

Once Sigma was divested of his book, Alice turned to the sole place the key that she had put together could possibly be used. With one quick twist of her wrist, the handcuffs fell away from the door of room '03'. The three of them explored this final room together. It had essentially the same layout as the other three rooms: bed, table, cabinet, phone. This time, however, the cabinet door opened easily. Phi picked up the item inside. It was a roll of aluminium foil; when she carefully unrolled it she found that the full length of the foil was nearly as tall as she was. There were darker lines running across the sheet of foil, dividing it into four rectangles. In each rectangle, darker areas formed strange patterns in the surface.

Sigma tapped Phi on the shoulder. "Hey, you're probably supposed to use this to cut it up," he said, handing her a box-cutter he'd taken from the table.

Phi did so, separating the four rectangles across the floor so that all could be seen clearly. Three of them had collections of vertical lines on them. Phi was just about to examine the fourth piece when Sigma picked it up, a glint of recognition in his non-artificial eye.

"Huh? This looks sort of like something I saw in room one…" Sigma turned the foil over so that Phi and Alice could see. Unlike the other three, the black markings on this one took the form of parts of geometrical shape.

Sigma led them back to room one and stood in front of the table in that room, still holding the piece of foil. Phi deliberately made sure to stand right in front of where Sigma had left the Schrodinger's Cat book, to prevent Sigma from getting his hands on it and starting to pun again. After comparing the foil and the table thoroughly, Sigma pulled the tray out from underneath the glass surface, laid the foil rectangle carefully on top, then slid both foil and tray back in. He beckoned Phi and Alice closer.

"See!" he exclaimed, "I was right. They did match."

Peering over Sigma's shoulder, Phi saw that where the grating above the table had looked like a bar code in her own room and in room three, here there were only four holes with various geometric shapes. Looking down at the foil, Phi could see that the dark areas of the wall were reflected faintly by the foil, completing the shapes already marked on the foil. Now, the complete image showed a circle, a five-pointed star, a square and a triangle.

Then Sigma sighed. "Okay, I'm not sure how we use that. It doesn't match any of the cabinet locks or anything."

Phi patted him on the back. "Don't worry, it was a clever idea. Maybe the other sheets of foil will work in the other room with the same trick, and we'll get more clues."

Trying the same trick in room three – with their second choice of foil rectangle, the first just produced gibberish – revealed a message reading 'LOCKER'. Which wasn't very useful, since the locker behind them was already open and empty: indeed, it was the locker they'd gotten the foil from in the first place. Still, it was confirmation that Sigma's idea would keep working, so they took the remaining two sheets of foil to room four: the room Phi had searched first. There, placing the foil in the tray caused the lines to form the numbers '3472'. As Alice took the remaining piece of foil to room two, Phi examined the revealed number: she guessed that this was the code to unlock the cabinet in room four.

As Phi turned around she saw Sigma standing enraptured in front of the poster of the woman, still covered by a silver layer. Phi tried to get his attention, but Sigma utterly failed to react to her; instead, his face was drawn, as if by a warped and unholy version of gravity, towards the image.

"The gods! I never thought I'd see one…" Sigma chanted reverently.

Phi was taken aback. "Uh… what?"

Sigma looked over to her, still gesturing grandly towards the poster that had captivated him. "You have to… scratch the silver parts off with a coin so you can see the naughty stuff. It's the ultimate in interactive poster technology! What teenage boy doesn't dream of something like this? The excitement! The anticipation! And finally, the reveal!"

Ugh. It seemed that Sigma was playing his 'dirty old man' act for all that it was worth. Well, you couldn't blame him. Men that age were usually set in their ways: immutable.

"You look… pretty excited," Phi said morosely, while desperately hoping Sigma wouldn't do anything… unforgivable.

Sigma stopped listening again. Phi returned to what she had originally intended to do before being… distracted: open up the locker. Despite the unusual setup of the number pad, Phi soon had it unlocked, and was able to look inside. On the floor of the cabinet was a weatherworn brown wallet. Phi opened it up, but there was only a single coin inside. It didn't take long for Phi to realise what the coin was intended for. A coin could easily be used to scratch the silver layer off Sigma's precious poster. Even knowing that it was part of the puzzle, Phi hesitated to use the coin. She feared Sigma's inevitably exuberant reaction to finding something that he could use to uncover the poster. Fighting her trepidation, Phi unclenched her hand, presenting the coin nervously in Sigma's direction.

Sigma pounced. Snatching the coin gleefully out of her palm, he went to work on the poster. His hand swept across the silver layer at a frantic, almost-superhuman speed. Phi tried to hide from the disturbing sight behind her hands, but it was only a couple of seconds before Sigma was finished, standing 'proudly' in front of his 'accomplishment'.

Sigma panted heavily. "I did it! Just look upon her glory!" After a couple more minutes of embarrassing behaviour, Sigma eventually calmed down. "Don't look at me like that, Phi," Sigma mumbled sheepishly, "See, there were clues here as well. Just look at her arms and legs."

Phi did so. On the limbs of the woman that Sigma had unveiled were lightly coloured symbols with numbers in them: a '6' in a star on the upper right arm, a '1' in a circle on the left arm, an '8' in a square just above the left knee and a nine in a triangle on the lower right leg. "Those look like the shapes from the foil in room one," Phi said, "We should take the poster with us and compare them."

Sigma leapt across and hugged her gratefully. "You mean… I can keep it? You're the best, Phi!"

"Ugh."

Phi and Sigma returned to room one, Sigma still holding tightly to his poster. When they arrived at the table, still containing the symbol-displaying foil, Sigma stuck the poster up on the wall above it, making sure not to obstruct the parts of the wall that were being reflected in the foil. As Phi had expected, the symbols of the poster matched those of the foil: circle, five-pointed star, square, triangle.

"That would make the code '1689'," Phi suggested. She turned around to type it into the button pad on the cabinet, but there was no response when she pressed the buttons. It was then that Phi noticed the difference between this cabinet and the one she'd opened in room four: this one had a keyhole above the number pad. "Damnit," she exclaimed, "Looks like we can't use this until we find another key."

It was then that Alice barged in, a frustrated look on her face. "Why the hell did you two just wander off like that?" she asked haughtily, "We're supposed to work together to solve this puzzle. Instead you just disappeared and left me to sort this out by myself."

"Hey, we were…" Phi started to answer back.

"Never mind," Alice interrupted, "I should tell you what I found. I was able to open the locker in room two and found a cassette tape inside, sort of like the ones used in old fashioned answer machines. I tried putting it in the phone in room four, and then in room two – which is when I found out you had wandered off – but their answer machines wouldn't open. I was able to put it in the cassette bay of the phone in room three, but for some reason it wouldn't let me listen to it. It just said 'This functionality is disabled' or something like that."

"Sometimes answering machines can be accessed by calling the phone in question from somewhere," Phi suggested.

"Yes, I knew that," Alice said, "That's why I came in here: to try and use this phone to call the one in room three."

"Let's do this, then!" Sigma exclaimed. He lifted the phone's handset to his ear and ran his hand along the buttons. "Looks like these buttons" – he pointed at the row of buttons above the display, which were numbered '1' to '4' – "are used to call the internal lines. I'll try it." Sigma's finger pressed down the button for internal line number '3'. Phi and Alice watched as Sigma listened. "What?!" Sigma said, slamming down the headset, "It says there's no number associated with that button. Why can't I call room three?"

"No idea," Phi replied, "Maybe you should try some of the other internal lines, see if they work."

This time Sigma pressed the button marked '2'. Phi waited for him to put the handset down, but this time he kept it firmly against his ear. "It's still ringing…" Sigma muttered.

Phi realised that she could faintly hear ringing coming from down the corridor. It must have been coming from one of the other phones: the phone in room two that Sigma was ringing. Alice strode out of the room; Phi heard the ringing stop as Alice received the call.

"Hey Alice, did that do anything?" Sigma asked into the mouthpiece.

Phi couldn't hear Alice's reply, but she was able to see Sigma's satisfied expression as he listened to Alice explanation of what she'd found. Eventually, he placed the handset back down and turned to Phi. "I'm gonna try calling room four now. You wanna head over there and answer it?"

Phi did so, arriving just in time to hear the phone start to ring. She picked up the handset and spoke, "So, Sigma, what am I looking for?"

She heard Sigma's voice being projected into her ear by the speaker. "Hey, Phi. Alice said she saw something on the phone display when I called her. You don't see something similar, do you?"

Now that Sigma mentioned it, the screen had changed. She read it out to Sigma. "Oh, right! It reads 'Agricola, agricola, nine, two'."

Sigma chortled. "How exactly did they fit an entire German-style farming simulation board-game onto the display?"

Phi was glad Sigma couldn't see how red her cheeks had gone with embarrassment. "Whoops. I meant 'Asterisk'." She slammed the phone down before Sigma could comment any further.

Phi and Alice reunited with Sigma in room one, just as he started to dial another number. "'2592'," he muttered, pressing each button in turn on the main number pad. After a pause, he spoke. "Goddamnit, that cassette tape's just a mocking message from Zero." Phi was glad that Sigma didn't relay the message to them: she's had as much of that annoying little rodent as she could handle. Still, Sigma muttered one little thing, presumably from Zero's spiel. "'Look at the left screen above the phone'?" Sigma paused as he glanced at the mentioned screen. "Oh! I get it: the number from the phone display's reflected in it like a mirror. Let's see, it reads: '2652'."

The moment he had the answer he slammed down the receiver, not wanting to listen to Zero any longer. Finally, he tapped this new number – 2652 – into the number pad. Rather than calling a phone, this number caused the cassette bay of the phone to spring open. Grinning with his success, Sigma claimed a small, key-like pin from the bay. To Phi, it was obvious where it had to be used. It seemed like they had everything they needed to open the last cabinet.

Once the pin was placed in the keyhole of the cabinet, the number pad sprung to life with a reassuring buzz. Phi quickly entered the number – 1689 – that she and Sigma had found by comparing the poster to the sheet of foil in room one.

The lights on the number pad flashed red. The cabinet didn't open.

"What the hell?!" Phi exclaimed. Then, she started to think of ways in which they could have gone wrong. They had to have made some mistake somewhere, and fixing it would be much more effective than merely hating the puzzle for having tricked her. "We need to have another look at that poster," she said.

"Wait. What's going on here?" Alice asked.

As Sigma explained it to Alice, Phi returned to studying the poster and the piece of foil below it. There must have been something that she had missed, some little thing that would change the numbers from what she had thought they were. She was certain that all concealment had been removed from the poster: Sigma's frenzied scratching would have taken care of that. She could clearly see all of the symbols clearly, matching the ones on the foil… wait! Phi worked it out at the exact same moment as Alice spoke up.

"Those symbols are upside down," Alice stated.

She was right. Where the five-pointed star on the foil had the central point facing upwards, the similar symbol on the poster was pointing downwards. The same was true of the triangle. That meant that what Phi had taken to be a '6' was actually a '9' and vice versa. The correct number was actually '1986'.

Finally, Phi was able to enter the number and open up the cabinet. Inside was a screen, glowing with a warm, successful shade of green. Just like the screen in the elevator puzzle, there was a three-by-three grid of symbols on it. Sigma, with his photographic memory, quickly memorised the safe password. Phi was just about to close the cabinet door when Sigma stopped her.

"Wait!" he shouted, "Do you remember how, in the puzzle earlier, we got a second password by putting in another memory card?"

Phi nodded, curiously.

Alice also understood what Sigma was saying. "Yes. That worked in the puzzle in my AB Room."

"I want to see if we can get something similar here," Sigma continued. He then pointed at a cable running from the screen to the door of the locker. "See? I don't think that number pad just unlocks the door. I think it controls which password appears on this screen as well."

"So, do you have any idea how to change the password on the screen?" Phi asked.

Sigma scrunched up his face in concentration. He held there for a couple of minutes, but then he nodded excitedly. "Oh! I've got it! This puzzle was all about reflection, right? Reflection in the foil, symmetrical rooms, the reflection of the room three phone number in the mirrors above it giving the actual solution. So if we reflect the first password, maybe we'll get another password?"

"It's worth trying," Phi replied. She visualised the password and the process of reflecting it in her head. "If you flip it horizontally, you get… no, that doesn't work. Try flipping it vertically instead: 1689… no, we've tried that already. Wait! If you do both, you get a rotation. Try 9861."

It was right. Soon, Sigma had memorised the blue-backed safe password as well.

Sigma opened up the safe with that password first, and handed the gold file he found inside to Phi. She opened it up and read one of the articles inside.

'Sigma's Cat Problem: Sigma has a strange verbal (and possible psychological) tic which causes him to make cat puns whenever he talks about cats. The cause of this behaviour seems to be an experience he had as a child.'

That was a strange thing to make a record of. According to the file, the cause of Sigma's incessant cat puns was a 'curse' that had been placed on him by a magical black cat. Phi didn't believe it. It was obviously an attempt by Zero to mock them. Still, it was strange that Zero had found out about Sigma's need to make cat puns. Sure, Zero would have researched all of his victims, but it would take quite a deep and thorough search to find information that specific.

"Find anything interesting, Phi?" Sigma asked as he opened the safe once again, this time with the main password.

Phi clamped the file shut. "No, nothing." There was no need to give Sigma any ideas.

The three of them looked at the items inside the safe. The first thing Sigma took out and handed to her looked like a map; Phi traced the outline of what looked like the warehouse with her finger and it seemed to match the actual walls of the warehouse, including six boxes that had to represent the AB rooms.

"It says 'Floor A'," Alice said, pointing out the label in the corner.

"We can look at it more later," Phi replied, curious to examine some of the other items in the safe, "Why don't we get all of it out before we start going through it?"

Sigma took a pair of cards out of the safe and handed one to Phi and the other to Alice. They were shining silver with a logo of a sun and the words 'Ambidex Room' printed on them in bold white text. "Now we can get into to AB rooms," he explained, "But how are we supposed to get back to the warehouse? That's where the AB rooms are! I'd wanna go back the way we came, but that door's locked."

In response to Sigma's question, Phi pointed out another sheet of paper in the safe.

Sigma picked it up and read it. "It looks like some more rules for the Nonary Game. It goes, 'Hare…'" Here Sigma chuckled slightly, though Phi didn't get what the joke was. "'… are a few more rules for you! Once you've opened a door, you can hop through it as much as you like… But! But but but, you have to escape before you can take advantage of this Free Rein Rule!" Sigma did an unnervingly good impression of Zero's voice. Phi guessed that he was able to imitate it so well, because he'd just listened closely to it through the phone.

Finally, Sigma handed a key to Alice. It was clearly the key that would open up the exit door at the far end of the corridor. Alice marched away down the corridor, intent on opening up the door and escaping.

Phi was about to join her, when Sigma stopped her. His hand clutched the Schrodinger's Cat book – Phi realised belatedly that Sigma had left it beside the safe – and he was looking at her intently, his sole remaining real eye doing a good impression of puppy dog eyes. No: pussy cat eyes.

"Hey Phi." Sigma was practically purring by now. "You know stuff and are really claw-ver. Purrlease, cat you tail me what's up with the catemathics in this purrecious…"

When she was asked later, Phi would reply that she acted in self-defence. She clamped her hand firmly over Sigma's mouth, smacked the book from his hand with a carefully aimed blow, then dragged him from the room.

This fanfic has branching storylines. To keep track of the whole big ball of yarn, a cat-flap to the Flow Diagram is provided in my Claw-thor Purr-ofile.

Yay cat puns!