The Modulo Tower

Sitting in the dark neon lit gaming room, he finished his 11th ice cream, his mind full of anxiety. “I hope she gets her hands on the game.”

The clock of his room ticked as he waited for Maytika Matte, his best friend.

Gamyeon Fin looked at the Alternate Reality Portal within his gaming room.

Alternate Reality Portal was a portal designed for the types of game which let you enter the game’s setting physically. The one that Gamyeon has, has pretty simple design, a rectangular hollow gate, it was the entrance. And on the back of it you could see a core insertion box for AR Games.

Alternate Reality Games are designed in a way that writes its codes within the space by the help of AR Portal by space manipulation technology of that era.

Each AR Portal has capability to create a localized space outside of our reality.

He was wearing a blue suit as if it were a special occasion. Sweat trickling down the temple despite the temperature of 18 degrees.

“Gam!!”

His face lit up, his lips curled up into a sweet and excited smile, “Comiiiing!” He rushed out.

Click! The door opened. Maytika Matte was standing, holding the box. As soon as she saw him, her face twisted with cringe. “What’s wrong with you? It’s a game. Why are you wearing a formal dress for this??”

With a smug grin, “Whatever! Let’s play quickly!!”

“Let me get in first!” She pushed him in, turned back and closed the door. “And go wear something simple dude. You can’t play like this.”

A few moments later, they were sitting in front of the box.

Maytika looked at the box. ‘13 Magical Games’ was written on it.

“Let’s start!” Gamyeon jumped at her and snatched the box. He opened the box; there was an instruction manual and a Cubical Core. Instruction manual was about, how to insert the core and start playing the game and some other basic instruction and rules for the games itself.

It wasn’t new, they had already played two Alternate Reality Games before this one, at least that’s what Gamyeon thought.

Maytika picked up the manual, “Let’s read this first--”

“No!” He snatched it away, “We gonna play now! We’ve been waiting for this game for almost a month now! We already know how to start the game let’s just go!!” He was bouncing with excitement, holding the core.

She extended her hand towards the core subconsciously, “Okay! Okay! I get it! Stop moving or you’re gonna break it!”

“Got it!” He sat down quietly.

With a sigh she sat calmed down as well.

A few minutes later, Gamyeon inserted the Core in the back of the Alternate Reality Portal.

The portal’s entrance lit up with white and on it, it was showing ‘The Modulo Tower’ written in cyan color.

“Modulo?” Maytika was surprised after reading that, for a reason she herself couldn’t remember.

“Let’s go!” He pushed her in.

“Wait--” She lost her balance and fell right through the entrance into the game and Gamyeon followed her.

The scenery changed from the dark neon-lit gaming room to a white colored room in a blink.

Gamyeon blinked again. “Woah…”

The room was cube-shaped, clean and almost too perfect, like someone copy-pasted the same wall four times and called it a design. Each wall had a black door with cyan lighting around it, glowing softly like it was waiting for them to do something stupid.

Three of the doors, one on left, one on front and one on right, had numbers written on them in cyan, 1, 2, 3 respectively and one door behind them had ‘Floor 0’ written on it.

Maytika turned her head to looked around. She looked below her and there was written 21 in white color on the hexagonal purple platform she was standing on. “21?”

They both stepped out of the hexagon. Just as they did that, they heard a ‘beep!’ sound.

They looked above the platform. And above the platform, there was a cyan colored timer running.

Gamyeon’s eyes shone as he looked at everything, “Whoa…” He was in strange awe to this perfection. He moved around and touched everything one by one.

He touched the door 1, or maybe it touched his heart, “Whoa! This is sick!! I want this type of door in my room!” He couldn’t stop smiling.

Maytika wasn’t less either, she felt strange kind of satisfaction after seeing this geometrical perfection, “This feels so intentional…”

[Time Left - 1:29:56]

Maytika looked above the platform, “1 hour 29 minutes and 56 seconds Left? I guess we need to finish this withing given time.”

“May!”

“What?” Matika looked at Gamyeon who was standing beside her.

He flashed a big smile showing his teeth, “How do we play?”

She was silent for few seconds before speaking, “That’s why I said “let’s read instructions.” There was tutorial for game one in it.”

He scratched his head with a nervous grin, “I guess we’ll figure out haha! I mean, who even needs a tutorial?!”

She sighed, “We have to reach a specific floor to clear this game, and this is the first one of the 13 games.” Maytika said.

“What? When did you read all that?” He eyebrows shot up in surprise.

“I just had a look before you snatched it away.” She shrugged.

He gave her a side eyed look, “Nerd.”

She gave him a stare, “What?”

“Nothing.” He looked away, “So, is there an elevator behind one of the doors?”

“Let’s check! Starting with door number 2.”

“No let’s go with one!”

“Nah!! We are going with either 2 or 3 first. I think door 1 might be a trap…”

“Really? Okay.” He shrugged.

May opened the door number 2 while Gam followed her.

They entered the room and closed the door. This room also had same design as previous one.

Maytika could see three doors one on left one on front and one on right with numbers, 1, 2, and 3 written on them respectively. And a central hexagonal purple platform with white colored 21 written on it.

“Looks same to me?” Gam grinned.

May’s face turned red, “No! Wait! First check the floor no. Maybe this room itself is a lift?” She pointed behind Gam, “Move aside let me look.”

Gam turned around to the door. Then turned back to look at her with a grin. “See?”

“Why is it still zero? Maybe if we go again with door 2, we will end up on another floor?”

“Let’s try.” He kept grinning.

They repeated this three times only to end up on ‘Floor 0’.

“What happens if we go back through this door with floor written on it instead of the numbered doors?” Gam smiled, “Maybe this is a shortcut to reach directly on top floor hahaha! I’m smart right?” He looked at her.

“Don’t be certain before even opening it. Open it.”

Gam goes to the door and tries to pull it… push it…

May laughed. “What happened?”

“Maybe I didn’t use enough force let me try again!” He tried and tried again but couldn’t open it.

“I guess we can only enter through that door into the room and not go to the previous one.” May opened up a small diary she brought with her and noted her observations so far.

“A diary? You doing math?”

“No. I’m just writing that we couldn’t open this door.” She closes it and looks at the 3rd door. “Let’s go with this one this time.”

They opened up the door and entered the next room only to find out they were still on the ‘Floor 0’.

“What’s going on?” May asked.

“I don’t know.” He shrugged, “But I’m telling you let’s go with number 1 there might and elevator there!!”

“I get it! Wait. Just one more time, we should go with door 3 please?” May asked.

“Sigh. Okay.”

They entered the next room. It was still floor zero.

May was standing speechless.

“Let’s go with one.” Gam pushed the door open.

And they entered.

May closed it.

The room still looked the same.

“Huh?? No elevator here either? No way! There should be a way to open the Floor Door!!” He turned around. “Move aside. I’m gonna open it!”

May stepped aside. Her eyes lit up as she looked at the floor number.

Gam mustered up all his strength and started pulling the floor door.

“Wait! It’s not floor zero! It’s Eight!!” May jumped happily.

“Huh?” Gam paused and looked at the floor door, “Oh yeah…we did it. We did it!!!”

“No, we didn’t. We just somehow reached 8th floor.”

“Aww come on! It’s still better than you.”

“Whatever.” She rolled her eyes and took out her diary again to note it.

“Let’s go! We gonna reach final floor with door number 1!!” Gam screamed in excitement.

They entered through the door number 1 again.

May looked at the floor number, it was ‘Floor 16’ now.

“It feels like adding 8 to the floor each time we enter through door one, right?” Gam asked her.

“I wouldn’t be certain with just two times opening it, but yeah, it feels like it.” She noted it down. But deep down, she wasn’t satisfied, she looked at him, “Hey, let’s go through door 2 again.”

“Whaaaaat? No. I know you’ll mess up. I’m a better gamer.” Gam teased her.

“Gamer? What part of this feels to you like a game? You’re just randomly opening the door 1 and expecting to reach the end!” She shot.

“Okay then. You go ahead with yourself with door 2 and I go with door 1. How does that sound?” Gam asked ignoring her.

“What? We’ll get lost? And the game has a time limit! What happens if we get lost and never reach in time together?! We don’t even know the rules!!”

He shrugged, “I don’t know! Why can’t we just go with my idea? You aren’t always right!”

Her eyes narrowed, “Alright, I get you wanna reach top floor but how do you know that the specified floor is the top floor?”

“I just know! It must be the top floor! I’m going through the door 1 now go to door 2.” He stuck out his tongue and rushed through door 1 again and slammed it.

“Ohh my God! Is he serious? Whatever. I’ll go through door 2. I guess.” But she hesitated. What if Gam never clears the game in time? They didn’t even read instruction manual. It was said to be an easy game but they can’t even figure out the rules.

She gulped and opened the door number 2. She stepped forward and didn’t close the door, shifted slightly to take a peek at the back of the door. But the floor number was black. She guessed, “Maybe I can’t figure the floor number until the door is fully closed.” She shut the door and now she could see at the floor number. “Sigh. I guess I really am a bad gamer…” It was floor number 2.

On the other hand.

“Wha- what just happened?!!” Gam fell into panic mode, his eyes widened and his eyebrows shot upwards. “Why did I end up on 3rd floor?!! It was the addition door!!” He looked at centre, the timer was running.

Negative thoughts started to emerge… What happens if he never gets out?! Do they get stuck here forever? He didn’t want to accept being stuck here forever. What if she was right?! He doesn’t even know the rules. He fell on his knees with a thud, and started pulling his hair while regretting his decisions.

His eyes darted towards the door number 2. “Maybe I should check it for once?” He was terrified after realizing he had been separated with her. He thought the other two wouldn’t work and she would come back to him by that door. “What if she’s waiting for me on floor 16?!” His breath turned shallow.

He clenched his fist, gritted his teeth as he looked at the floor door, and then finally rushed to the floor door and tried to open it. He poured all his energy, as he did that, his hands slipped and he fell backwards and slammed his head on the hexagon, “ARGH!!” He cried. All his efforts went in vain…

He steadied himself and stood there motionlessly with same expressions on his face.

[Time Left - 1:02:47]

He was standing frozen. Tears fell through. “Oh my god… I’m stuck… Where do I go now? Which floor do I need to go?” He felt helpless. He needed to do something, his heard turned to looked at the door 2. A thought settled in his mind and he decided he’ll give the door number 2 a try.

He shook away all his thoughts and just pushed through the door 2 and slammed it to checked the floor number. His face went pale, “No…” It was still ‘Floor 3’…

“What…?” His face twisted into anger, then confusion, sadness.

He looked at the floor number again. Still 3.

“No way… that makes no sense.”

He opened Door 2 again. Slammed it shut.

Still ‘Floor 3’.

Silence hit him a little harder this time.

“…Okay, okay,” he muttered, forcing a laugh, “This must be some glitch right…?”

But his hands were already shaking. “There’s no way… did I really mess it up?” He gritted his teeth, “If door 2 doesn’t work, why is she not here yet? Where is she?!”

The room was completely silent, “What if… What if this is all actually a trap and it is actually just random floor?”

“What if we are just looping on same floor and these are just lies?!”

“Or what if the floors themselves are repeating and we never leave it?!!”

He shook his head and tried to calm himself down and tried looked all over the room to find some hint that would help him in some way.

His gaze shifted towards the centre of the floor. “21?” He suddenly remembered her words “how do you know that the specified floor is the top floor?” a subtle smile emerged at his face, “I guess this 21 is the floor we have to reach?” Because it was written on every floor, he couldn’t figure out it’s significance other than this. “From what I can understand, the floor two and three don’t work.”

He took deep breaths, calmed himself down.

On ‘Floor 2’.

May noted down the observation in her diary and guessed, “Maybe this is the subtraction door? No, it couldn’t be…” She paused “No. Maybe it is. What if I reach zero again after going through this door? Because we can’t go into a negative floor number so we go back to zero and that’s why we end up on zero?”

She looked in her diary, “I went from ‘Floor 16’ to ‘Floor 2’ that means it might be [negative 14] door or the [divide by 8] door” She tapped her chin with her pen, “One thing is certain, the ‘Floor number’ is used in the equation.”

She closed the diary, “If floor number is ‘n’ then the equation for door 1 is [n+8] by my observation. And if three arithmetic operations are used that they might be addition subtraction and multiplication or division. So, the equation for door 2 might be [n-14] and for door 3 might be [n multiplied by some constant]”

But she was still unsure, “What if it’s just simply random?” She decided to check door number 1 again to confirm her suspicion about [n+8].

She entered through the door. It was now ‘Floor 10’.

“I was right!” She said excitedly. “It’s just basic math. I can do it!”

On ‘Floor 3’.

Gam entered through door 1 and checked the floor door. It said ‘Floor 11’.

“Huh? It feels like addition… but then what happened before? Why did I end up on 3rd floor abruptly?” He couldn’t figure out why it happened but he felt relief and was now sure that door 1 was right door to reach the end.

[Time Left - 0:41:01]

May’s eyes darted towards door 3, “I should check what happens after door 3.” She entered the door number 3 and checked.

It was ‘Floor 16’…

“16? What? Not multiply. Not Division. Addition? No… It can’t be addition. If it was, it would have worked on first try. I guess my assumptions were wrong?”

She couldn’t wrap her head around what was going on, sometimes she felt it was random and sometimes she felt it had some logic. But deep down there was a feeling, the feeling that told her that she was missing something important…

She decided to go back at ‘Floor 2’ to test it again. She pulled out her diary and noted her observations first, then rechecked how she went to the ‘Floor 2’ from here. “Right.” She nodded and then opened up the door number two.

She looked around on the floor for some hint because every floor looked identical just the floor number was different.

Her eyes darted to the hexagonal purple platform, “… 21… what does this mean?” She looked towards the floor door. She took a pause and, “If this means number of floors in this tower, The Modulo Tower, then that means final floor should be floor number 20 as first floor was floor 0…” She sat down and put her fist under her chin with one eye closed. “Hmmm… Modulo sounds familiar… What could it be? Where have I heard it before? I can’t remember.”

She stood up and decided to enter door 2 to test what happens, “Maybe some pattern emerge?” last time she reverted back to floor 2 from floor 16, so normally she thought it was division or the subtraction door.

She entered through it and checked the floor number. It was the ‘Floor 16’.

Her brows furrowed and her forehead formed wrinkles, “What? Why? Only door number one feels consistent. Should I only go with door 1? Was Gam right all along? But… If I go through door one again and again, I will end up on floor 18th then how am I supposed to get to floor 20? If I go again through door 1…” She froze…

“Modulo…” Her eyes widened as it clicked to her. “Modulo Operation!!” She slammed her right fist on left palm with a determined smile.

On ‘Floor 11’.

Gam entered through the door 1 again and then looked at the floor number.

“Floor 19.” His brows furrowed, “But wait. I need to go to 21st floor. And this is [+8 door]. How am I supposed to go there…?”

While he was thinking, he subconsciously entered through door number 1 again and then checked.

“…” He froze, his moth was left open, a bead of sweat trickled down his forehead. “What? Floor 6?!! Why?!! What happened again?!!”

He gritted his teeth and slammed his legs hard on ground “This is so frustrating! And why isn’t May following me?! Is she stuck in the loop of door 2?! I didn’t think she was so dumb! Hmph!” He scratched his head so hard that he pulled a few hairs.

He folded his arm and tried to think why did it happened. “From ‘Floor 19’ I got back to ‘Floor 6’. Oh, wait so, is it like this?” His eyes suddenly widened in realization, “It is [+8]. It’s just that floor limit is 21 so after 21 it counted back from 1 haha!”

He paused for a moment, he was still doubtful he checked in his head again, and a smile emerged on his face, “Whoa it was so simple! It’s like the ancient games that were played during 20th century. Where after completing all the levels you go back at level 1! This was so simple! So, I just need to keep going until I reach 21?!! I figured it out!!! YEAYYYY!!!”

He was jumping all over the room in heat of excitement. “Damn! I was right all along!! I knew May was wrong!!” He clenched his fist as if he had won something.

On ‘Floor 16’.

[Time Left - 0:26:03]

May was standing at the centre of the floor 16. “So that’s why it is called The Modulo Tower, it was ‘Modulo Operation’ after all. No wonder I keep reverted back.” She nodded in satisfaction, “Then if that’s the case I should look at the pattern emerged with this revelation.” She opened up her diary, where she has written down the sequence and important details. The pages were already messy with numbers, arrows, and scratched-out guesses.

“Hmmm… the first time I used door 2 It was on ‘Floor 0’ and we didn’t end up anywhere. So, by that logic, it should either be Multiplication or Division. Second time I used it was on floor 16 and I ended with floor 2. Which makes it look like it is [n divided by 8] door. But then again, I used it on floor 2 and ended with floor 16, by that logic it should be [n multiplied by 8] door.”

She smiled, “And now comes the interesting part. If we assume this tower work on Modulo (21), and then I assume door 2 to be [n multiplied by 8] door. And apply it on the ‘Floor 16’, that is, [16*8] = 128. We end up on floor 2 again, as modulo (21) of 128 equals 2.”

Now she looked again at diary, “And that leads to, the final door, door 3. What could it be? One is addition. One is Multiplication, so third one needn’t be a reducing arithmetic. Maybe it is something like n to the power of k? But then what is ‘k’ here?”

She sat down with fist under her chin, brows knitted together. “That’s still assumption… But the thing is, if I stick to certainty, we will not be able to complete this game on time. What happens then? Do we get stuck?” These thoughts were making her sweat.

“Maybe the ‘Failed.’ screen appears and throws us out?” She chuckled and then instantly shook her head and returned her focused into the diary. “There’s no time to think about that now.” She tightened the grip on her diary.

[Time Left - 0:13:09]

She flipped through the pages, “Now onto the main point. First time I used the door 3, it was also on ‘Floor 0’ and we still ended up on same floor. The next time I used door 3 was on ‘Floor 10’ and I ended up on ‘Floor 16’… If ‘k’ equals 2, then 10 squared is 100… and that matches with the observation pretty easily as modulo (21) of 100 equals 16. I’m not sure but I guess it’s best to assume that door 3 is [n squared].”

On ‘Floor 6’.

Gam entered through door 1 again. “It’s floor 14 now. Damn it! I got so less time. I need to be quick.” He opened the door 1 and entered through it. “Now I’m on floor 1. Let’s go!”

Deep down he was anxious. “What happened to May? Where is she? Why is she so slow.” His hands were shaking as he opened the door. “I’m at floor 17 now…” He paused and turned back to look for her, just in case she was coming. “She’s not here yet. Should I wait?” He gritted his teeth. “But the time is running out? Is she doing this on purpose?” He shook his head and slapped himself on cheeks with both the hands.

[Time Left - 0:06:57]

On ‘Floor 16’.

One could hear scribbling noises of paper and pen. That was because May was calculating shortest possible path to reach floor 20.

“I’m on 16, if I go through door 3 then I get 16 squared that is 256, it’s modulo 21 is equal to 4 so I’ll reach floor 4, then it will become simple, I’ll just go through door 1 two time and reach the floor 20…” She closed the diary.

She looked towards the door 1. Every second passes, her heart beats faster, the worry couldn’t leave her mind. “I hope Gam has figured it out. I’m not too scared because even if he chooses door 1 each time he’ll end up on floor 20 eventually but what I’m scared about is, if he doesn’t reach on time…” Sweat trickled down her temple as her eyes narrowed, she clenched her jaw tight…

She closed her eyes and took a few deep breaths, “I’ll wait at the floor 20. I hope this game isn’t a competition type game.” She entered through door 3 and then looked at floor door. Her eyes lit up, “Yes! It is the [n Squared] door. I’m on floor 4. Now I just need to go through door 1 two times.” She was happy that she figured the game out. “Even though mathematical games are worst match for Gamyeon, this one is very easy so I hope he does not reach late. Or maybe he’s already waiting for me?” She entered through the door 1 and reached on floor 12. “And now comes the final question. Is Gam waiting for me on the next floor?” She made her stride towards the door 1 and opened it.

[Time Left - 0:00:50]

The room was empty, there were no door number 1, 2 and 3 this time and a timer running on center just like all the floor. On the front of floor door there was screen showing [1/2 cleared]. She closed the door and looked at floor door. It was showing a glowing ‘Floor 20’ in cyan color.

“I’m on floor 20.” She turned around, “It’s showing 1/2 and nobody is here that means Gam is still on his way… only 41 seconds are left.” Her face went pale.

[Time Left - 0:00:30]

Gam opened door number 1 and entered the floor 4. He slammed the floor door and didn’t try to look at it.

[Time Left - 0:00:17]

He was sweating as he rushed to door one and opened it and entered. He was on floor 12, he slammed the floor door.

[Time Left - 0:00:08]

And again, rushed to opened door 1.

[Time Left - 0:00:02]

He finally entered floor 20.

[2/2 Cleared.]

[Processing…]

[VICTORY!]

[You may EXIT ‘The Modulo Tower’ by standing on the Hexagon at the centre of the room.]

May turned her head. “You’re here. I thought you were lost.”

Gam was in disbelief. “What?!! How did you reach here faster than me?!!!”

May grinned, “It was easy.” And swayed her hair with smugness. “I figured out this tower works on Modulo operation. And each door had its own equation.”

He tilted his head, “Modulo what? Is this hospital?”

A pang of irritation ran through her face, “Not that operation. I mean mathematical operation.”

Giving her a side eye, “Nerd.” He spoke.

“What did you say?” Her eyes narrowed with one brow up.

He shook his head, “Nothing. Anyway. But I thought the door 2 and 3 don’t work?”

“Did you even try?” She asked while being displeased.

“I did!! I tried the door number 2 on ‘Floor 3’ and then I got back into ‘Floor 3’!!”

“…” She patted his head. “Let me explain. The door 2 is multiplication door. The function that governs it is [n multiplied by 8], so putting 3 into the equation we get 24 and we know modulo of 24 is still 3!” Gesturing three with her hands.

“How would I know?” He replied with a plain face.

“Okay okay I’ll make it simpler just for you. Modulo operation helps you get remainer of a number. Suppose you have 24, then modulo (21) of 24 means you need to divide 24 by 21 and get the remainder, and the remainder gives you the floor number.”

He put his hands on his chin, as if thinking hard, “Then shouldn’t we get floor zero if we divide 21 by 21, how did you end up on floor 21?”

“21? What are you going on about? This is ‘Floor 20’.” She frowned.

“What?” He looked back at the floor door “Oh…” he turned to her, “Then why was 21 written on the floor?”

“Because there are 21 floors you idiot. Starting with floor 0.”

The sudden realization hit him, “Ohh so that’s how it is! It’s starting from floor 0 so the 21st floor is the floor 20!” He facepalmed himself, “How come I’m this bad at math?”

“God knows.” She shrugged.

“But you know what?” He showed his big smile while flashing his teeth.

“What?” She frowned.

“You suck at explanation.” He chuckled.

She tilted her head, “What why?”

“I have a better explanation. A clock. No. A 21 hours clock, starting with 0. Just like our usual 24 hours digital clocks. They reach 0th hour after finishing full cycle.” He grinned while giving her a side eye.

“Yeah. After 23:59:59 it becomes 00:00:00. Good explanation. But I won because I reached before you.” She teased him back.

“Yeah yeah…” He waved his hand as if ignoring it.

Her stomach growled and she looked away as soon as her face turned red, “Anyway, let’s get back. I’m tired and hungry.”

“HAHAHA!! Alright!”

They both stepped on the purple hexagon.

[Leaving the game…]

Thud. Maytika fell down on the floor, “I’m so tired!”

The white screen of the portal went off and the portal closed.

May stretched her arms while lying on the ground, “Do you have some cold drink and chips?”

“Yeah. They’re in the kitchen, get some for me too.” Gamyeon was also lying on the floor.

“You go!”

“You!!”

“I’m taking a nap we’ll play the next game after I wake go get me snacks till then.”

“No! you go!”

She pouted, “But, I’m a girl.”

“That’s why! Ladies first.” He gave her a thumbs up with a wink.

“…” She shot him a cold stare.

“Okay, okay. You’re scaring me.” He pushed himself up with a sigh. “I’ll go. And I’m not coming back quickly.”

“Whatever.” She shrugged.

The room went silent for some time, Maytika was alone.

She looked up at the ceiling, “That was fun. I love maths. I bet Gam enjoyed too.” She chuckled, not knowing what 13-year-old Gamyeon had suffered through in ‘The Modulo Tower’.

But at last, it was over without a tragedy.