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SNAPCRAFT | Ch. 7.5 - Fibonacci Sequence
🕑 Added 2023-11-23 08:03:11 +0000 UTCHey, everyone! This is a bonus chapter. Would you like to see one like this after every round to see how other sectors tackle Snap Craft? Let me know in the comments!
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A figure appeared in the woodland. A grey tunic with a blue hexahedron marked her as a sixth-tier mathematician. Her black and grey hair cascaded over her shoulders, and she had what she liked to think was impeccable skin for a woman her age. She was Helen from sector 1J and, as laws of probability would have it, a second-time trial runner.
Helen felt the weight hanging on her neck and ran her bony hands down the strap until she found the machine Daisy had strapped to her. The mathematician looked around her and saw trees as far as her eyes could see. Feeling her heart racing again, she cleared her throat and began chanting the number for the second time today.
“One point six one eight zero three three nine eight eight seven…”
Just like it had happened in the white room, as soon as the sequence came out of her mouth, her heart rate slowed, and her mind regained its keen edge. The tension of the impending exams lost its power over her as she recited her old friend who had kept her company countless nights. Even though Pi was the overall favorite in sector 1J, she was more of a golden number kind of gal.
She mumbled as she examined the sight around her and then studied the heavy device tied to her neck. “A camera,” she said. The statement interrupted the chant of the golden ratio, but she was calmer now and always thought better when she spoke her thoughts aloud. “These haven’t been around for decades.” She picked it up and looked into the viewfinder.
Comparing the viewfinder's length and height, she found their ratio was the same as the ratio of their sum to the larger of the two, in this case, the width: the golden number. “You can’t help yourself, can you, Daisy?” she teased.
Finding a pattern so soon boded well. It was a sign that mathematics would be a significant part of this year's exams. But before she could search for more patterns, a general assessment of the exam’s rules was in order. Obviously, the camera was a crucial element in this trial. She took a picture of the nearest tree.
Capture successful!
Tries left: 19 of 20
Time left in Snap Arena 1:59:42.
She noted the time available to her. Two hours was very little. Likely, there was going to be another part to this challenge. Mechanical noises rang from within the device, startling her, and the camera spat out a card.
Pine Tree (Common)
4 of 5
Hp: 2
Vp: 1
“Fascinating.” The card had several numbers. Presented with one more piece of evidence that numbers and mathematics would be important this year, she smiled at the thought that this might be her time to shine. When she last participated, the odds hadn’t been in her favor. It was one of those dreadful exams where she was forced to interact with other sectors. Interpersonal skills were not her forte, nor her people’s. This time, she would do better.
Now that she understood the gist of the game, she searched for patterns. Beneath her feet, there were countless fine needles. She judged them countless because, unfortunately, she didn’t possess the gift of subitizing, which would have allowed her to count all the pine needles with a glance. She had to do it the hard way.
She focused on something more manageable: the trees. Fixating her gaze on a distant tree, and without moving her head, Helen counted thirteen trees. She turned her head ninety degrees and repeated the process, counting twenty-one trees. She did this one final time, counting eight trees.
It was just as she had suspected. The Fibonacci sequence. Daisy had included it everywhere in the arena. She tried not to get too excited. One of the problems her people often faced in the trials was being too literal. If one looked hard enough, one could find mathematics anywhere.
But it couldn’t be just a coincidence. There were too many signs around her: the proportions of the camera, the layout of the trees, and the choice of pines as the predominant tree in this arena. After all, pine cones and their spirals were one of the best examples of the natural Fibonacci sequence.
She had found the pattern. Now, it was time to make use of it. She already had the photograph of one tree. She leaned her face against the camera and tried to frame a location where she could only get two trees. After many adjustments and a lot of walking, she finally found a particularly empty patch of woodland where she could make the shot.
Capture successful!
Tries left: 18 of 20
Two Pine Trees (Common)
1 of 5
Hp: 2
Vp: 2
Seeing the numbers in the cards, she smiled. “One, two and five. All part of the sequence,” she praised. It was another reassuring sign that she was in the right direction. She moved on to look for a place where she could find three trees. For some reason, it was even harder than finding a place with two. Finally, she was able to capture only three trees.
Capture successful!
Tries left: 17 of 20
Three Pine Trees (Common)
1 of 5
Hp: 2
Vp: 3
Although one, two, and five were all in the Fibonacci sequence, seventeen and twenty weren’t. The lack of harmony sickened her, but she reined in her thoughts. She shouldn't get too caught up in the numbers. Sometimes, things were just random or had a logic of their own.
She focused on what belonged to the pattern and discarded all other disquieting thoughts. She added three to the previous number in the sequence, two, to get the next one: five. She looked for an angle where she could spot five trees. That was considerably easier.
Capture successful!
Tries left: 16 of 20
Five Pine Trees (Uncommon)
1 of 4
Hp: 2
Vp: 4
Glad to get another element of the Fibonacci sequence, Helen searched for spots where she could photograph eight, thirteen, and twenty-one trees in one shot.
Capture successful!
Tries left: 15 of 20
Eight Pine Trees (Uncommon)
1 of 4
Hp: 2
Vp: 5
Capture successful!
Tries left: 14 of 20
Thirteen Pine Trees (Uncommon)
1 of 4
Hp: 2
Vp: 6
Capture successful!
Tries left: 13 of 20
Twenty-One Pine Trees (Uncommon)
1 of 4
Hp: 2
Vp: 7
The more she climbed in the sequence, the more one of the numbers went up. She took that as a positive sign and tried to find the right angle to photograph thirty-four trees. In a dense patch of woodland, she squeezed the needed trees in one shot, obtaining the last piece in the mathematical puzzle.
Thirty-Four Pine Trees (Rare)
1 of 3
Hp: 2
Vp: 8
The next number in the sequence was fifty-five. She dropped the idea of finding it, though. It had been hard as it was to find a spot where she could frame thirty-four pine trees. How in the world would she get fifty-five?
It wasn’t a bad outcome. She had cards for eight of the numbers in Fibonacci’s sequence. Since eight was also part of the sequence, it neatly closed the circle and created a beautiful symmetry.
Now, it was time to look for more patterns in the map. The pine cones were green and hidden beyond her view, like a treasure guarded by an army of branches and green needles. She approached one of the trunks to try to climb it, but her hands just went through the tree, causing her to yelp. What a strange rule! It looked like she couldn’t interact with the map, and the pine cones were beyond her reach.
Perhaps it was time to investigate the arena itself. She walked as far as she could until she bumped into the invisible wall that marked the arena's edge. Then, she studied the surface, discovering that it angled slightly. She took a few steps along the invisible wall and felt the arena's curvature.
“A circle. Very well,” she said happily. She loved circles, a simple testimony to the perfection of mathematics. Now, it was a matter of figuring out what secrets lay within.
With her back against the wall, she took off, running in a straight line. After a few minutes, she crossed the circle. She estimated the circle's diameter by counting her steps and knowing how wide her stride was. Helen then turned ninety degrees to her right and began crossing the arena again.
After doing this three times, she found she kept passing a dead tree. That had to be the center of the circle. The tree itself was different from all others. Approaching it, she found beds of mushrooms. Eight mushrooms here, thirteen mushrooms there. More signs of the Fibonacci sequence.
Her mood lifted at each realization that this arena had a heavy mathematical element. She was on the right track. Discovering the shape and dimensions of the circle was important. With it, she could now keep exploring the pattern further. She squinted, straining her mind as she tried to recall how to make a Fibonacci spiral. After a few moments of mumbling old Math lessons and one recitation of the golden number, she finally remembered.
With the tree as the center, she took one step. Then, she turned clockwise and took two more steps. She turned right again and took three, followed by stretches of five, eight, thirteen, and twenty-one steps. Following this sequence, she would travel the arena in the rough pattern of a Fibonacci spiral.
After walking a hundred and forty-four steps and before she turned right and began the next stretch, she found something she hadn’t seen anywhere else in the arena. It was a pinecone that had fallen on the ground. She tried to grab it, but her hands just went through it. Whatever, she would just take a picture of it. She carefully chose an angle that captured the spirals forming from the pinecone’s base and took a photograph.
Capture successful!
Tries left: 10 of 20
Spiral (Rare)
1 of 3
Hp: 1
Vp: 6
She smiled happily. Daisy had hidden valuable resources at these specific points of the Fibonacci spiral. Now that she had found the pinecone, she turned clockwise again. She would now walk two hundred and thirty-four steps to the next point in the spiral.
She patiently followed the pattern, and after two more turns, she found something unique. It was a beautiful scene. Rays of light shone down on the woodland floor, filtered by the needles of the pine trees. The scene was so enchanting that she couldn’t help taking a picture of it.
Capture failed!
Strange. She had thought this was something important. Oh well, maybe she had missed something. There was a ring, and she was suddenly transported out of the arena and back to the white room.
It looked like time had sneaked up on her. The two hours for the exam were over before she noticed.
The room had something new compared to the last time she was here. It was a table. She approached it and smiled again, realizing that its depth and width were also in the golden ratio. Perhaps this is why they called them irrational numbers: they made Daisy behave irrationally.
“What am I supposed to do here?” she asked as she ran her fingers through the table. She found the two engravings. Their sizes corresponded to the cards she had gotten in the arena. Where were the cards, though? She searched her pockets and found nothing.
“Inventory,” she called. A floating window appeared. This feature was present in many exams, so she wasn’t surprised. It had also been available the first time she was in the exams. She grabbed all the cards and put them on the table, neatly organized by numbers in the Fibonacci sequence, with the [Spiral] card to the side.
Logically, she had to place the cards on the engravings. In what combinations, though? And what sequence should she follow? “Daisy, you’ve made these trials exceedingly easy this year.”
[Pine Tree] + [Two Pine Trees]
Pine Tree | Hp: 2→0
Two Pine Trees | Hp: 2→2
Crafting failed!
“Did I do anything wrong? Why does it say I failed?” she asked while studying the cards she had just used. The [Pine Tree] card became dull, and one of its numbers dropped to zero. The other card, however, saw an increase in one of the other numbers.
Two Pine Trees (Common)
Hp: 2
Vp: 3
“The second number rose! That means that it can’t be really a failure. Can it?” She prized numbers over words, so she decided to soldier on. She got the next card and placed it over the engraving pattern. The table lit, merging the cards.
[Two Pine Trees] + [Three Pine Trees]
Two Pine Trees | Hp: 2→0
Three Pine Trees | Hp: 2→2
Crafting failed!
The [Two Pine Trees] card became dull this time, whereas the [Three Pine Trees] card had changed.
Three Pine Trees (Common)
Hp: 2
Vp: 5
It looked like she could advance the number of points of the higher card to the following number in the sequence by emulating the Fibonacci Sequence in the table. Even though the difference now was tiny, the more she progressed, the more significant the gap would become.
She kept methodically grabbing the cards and running through the sequence she had seen so much of in the woodland.
[Three Pine Trees] + [Five Pine Trees]
Three Pine Trees | Hp: 2→0
Five Pine Trees | Hp: 2→2
Crafting failed!
Five Pine Trees (Uncommon)
Hp: 2
Vp: 8
[Five Pine Trees] + [Eight Pine Trees]
Five Pine Trees | Hp: 2→0
Eight Pine Trees | Hp: 2→2
Crafting failed!
Eight Pine Trees (Uncommon)
Hp: 2
Vp: 13
[Eight Pine Trees] + [Thirteen Pine Trees]
Eight Pine Trees | Hp: 2→0
Thirteen Pine Trees | Hp: 2→2
Crafting failed!
Thirteen Pine Trees (Uncommon)
Hp: 2
Vp: 21
[Thirteen Pine Trees] + [Twenty-One Pine Trees]
Thirteen Pine Trees | Hp: 2→0
Twenty One Pine Trees | Hp: 2→2
Crafting failed!
Twenty-One Pine Trees (Uncommon)
Hp: 2
Vp: 34
She kept grabbing card after card until she finally reached the last one.
[Twenty-One Pine Trees] + [Thirty-Four Pine Trees]
[Twenty-One Pine Trees] | Hp: 2→0
[Thirty-Four Pine Trees] | Hp: 2→0
Crafting successful! You’ve crafted [Pine Woodland].
Recipe book unlocked! New recipe added to your recipe book.
Pine Woodland (Legendary)
Hp: 0
Vp: 55
The thrill of harmony! Helen picked up the shiny new card. It looked like the participant with the most points would win the exams. In that case, she was feeling confident about getting a good score.
When her people chose to go all in on Math three centuries ago, they knew it was a considerable risk. The logic had been that the laws of math bound Daisy. By mastering the laws, they could master Daisy. Their investment had paid out. Math did work. Sector 1J had been a thriving sector with a large population and several exams under their belts.
Their specialization did nothing for them in some years. Still, they had an overwhelming advantage over their competitors in others - 31,41% of the time, to be exact, mathematically poetic as that may be. It looked like the odds were in their favor this year.
