Chapter 1 - "Who are you?"

Feridun Yüksel's Team

Plevne Secondary School

Lapseki / Çanakkale

Cemre, Defne, Deniz and Beril were very good friends. They were all in the same class together. Their favorite subject at school was math. Their math teacher was teaching them math in a very fun way. One day their teacher told them that she was going to give them a test on fractions and ratios. The friends wanted to prepare very well for the test. So they decided to study at Cemre's house.

There was a table in Cemre's room, and there were lots of books, notebooks and pencils on the table. The friends sat around the table and started to study. They were repeating the topic of fractions and proportion. But after a while they started to get distracted. Because there

were very interesting things in the room.

Cemre's father was a collector and antique dealer. There were many old and valuable things in the room that his father had brought. The friends enjoyed looking at them very much. 

The most interesting thing in Cemre's room was a big mirror. The mirror was very old and beautiful. The frame of the mirror was carved and gold-plated. The glass of the mirror was very shiny and smooth.

The friends stopped studying and stood in front of the mirror. They began to watch themselves in the mirror. The mirror was so big that it could easily show them all.

 Suddenly something very strange happened. It was as if the mirror started to move. The images in the mirrorblurred and disappeared. The friends looked at each other with puzzled and frightened eyes. Then suddenly they felt themselves being pulled through the mirror. The children found themselves in the middle of a forest. The forest was very dark and mysterious. It was full of trees with lush green leaves and dense undergrowth. The children were terrified, what had just happened, what were they going to do, how had they gotten here? Cemre immediately started looking for the mirror, but there was no mirror and no clue as to how they had gotten here. Then a voice was heard:

"Hey! Come here, follow the river!" Deniz asked, "Who are you?" but got no answer.  "But there is no river here!" said Beril in a tearful voice. They were all worried, but Cemre heard the sound of the water and said, "This way, girls." As they started walking forward, they saw a river in the forest. The river offered a beautiful view with its crystal clear water. 

Defne said, "What are we doing now? Where are we, are we in a dream, where are we going, whose voice was that?" she asked in a worried voice. 

Cemre, the coolest of the group, said, "We have no other choice, we have to listen to the voice. We have a very big problem, but to solve it we need to understand 

what the problem is, as always." 

Deniz nodded and said, "For that, we need to stay calm and collect the data!" Four friends, Cemre and Deniz, decided to follow the river and eventually found a village.  

The village consisted of wooden houses and had a few small shops. There was a big square in the center of the  village and in the middle of the square stood a big and strange statue of a dragon. 

At the foot of the statue they saw a thin, tiny, half unconscious child. Cemre asked, "Who are you?" 

"My name is Talay," the boy said with difficulty. "I brought you here, I'm sorry but I needed you." 

"Why?" asked Defne, she was angry and had found someone to vent her anger on. Beril calmed her down and asked, "What happened to you?" 

Talay said, "I spent almost all my strength to bring you here and I could only call out to you with the last of my strength. Now I need to get some rest." 

Defne snapped, "What do you want from us?" 

"Just some math, but let me rest and I will tell you everything," Talay managed to say before passing out.

The children's emotions were turned upside down. They were frightened and desperate at the same time. They were angry and yet curious at the same time. Talay was the only one who knew what was waiting for them, but he was also unconscious. 

Cemre said, "Calm down, our teacher used to say: "Every problem has a solution. Enjoy it and try to understand it."

Maybe a very fun adventure awaits us!" she said, actually scared herself. Still, she wanted to encourage her friends. 

Defne said, "I hope you are right, Cemre. But why did that boy call us math? What does math have to do with us being here?" 

Deniz said, "Maybe math is a very important thing in this dimension. Maybe people here don't know math. Or maybe math works very differently here." 

Beril said, "What do you mean? Isn't math the same everywhere?" 

Perhaps the answer to all questions lay on the ground.

Chapter 2 - Difficult Decision

Mohammad Darabseh's Team

Mo'ath Bin Jabal Primary School For Boys

Ramtha/ Jordan

After a while Talay came to and told the story: "This was my city. Elves, dwarves, wizards, in fact all of us lived here in peace and tranquility. But then Abra the Wizard came and took the king and queen of our country, my father and mother, hostage. He enslaved all the people and started to exploit our energies. There is only one way to get my parents out of the dungeon and save the country from Abra: Destroy Abra's magic. And for that we need math, because the dungeon doors will only open if we solve the riddles." 
 Defne interrupted: "What does any of this have to do with us? Why are we here?" 
 Talay said, "Because Abra magically took our math skills

away from us. I searched all over the universes for someone like you who is interested in mathematics and as soon as I saw you, I had to lure you here because I was nearing the end of my energy and I couldn't waste time. I apologize to you for that. I hope you will forgive me." 

 The children felt sorry for Talay, but they also had to think about themselves.

"So, how do we get from here to our house again?" asked Beril. 
 "I need to cast the spell again to open the door that will take you home, but unfortunately I am very tired and opening doors is not an easy task. And every time Abra is here, our energy diminishes. That's why we must get rid of her as soon as possible. You will help me, won't you?"
 "What if we don't or can't help you?" Deniz asked. 
 "I would like to send you back, but I don't think I have the energy to open the door. Our only option is to get my family out of the dungeon and save the country from Abra. I'm sorry."

Defne was about to jump on Talay at this answer, but Beril held her back: "How dare you condemn us here when we don't even know if we can help you. Are you worse or Abra? Get us out of here immediately and send us home!" As Defne was shouting, she heard Cemre's voice saying, "Okay!" "Okay, we will help you and we will get out of here and go home. There is no other solution anyway!" Cemre said. Deniz nodded. After a short silence, Defne and Beril agreed with Cemre. 

Talay was very happy and thanked them. "Then let's get going right away. The road to the dungeon is long and dangerous. 

But I believe we can make it with you." He left the village with his friends. As they made their way to Abra's dungeon, they wondered about the riddles and adventures that awaited them.

 "The road to the dungeon leads to a cave in a mountain far from the village. There are three ways to get to the cave. One of them is flat, uneven terrain. However, the road is 24 kilometers long and we can travel 6 kilometers

per hour. The second one is a bit more hilly, we will have to cross a few large and small hills. Our speed will drop to 5 km/h, but the road will be 19 km long. The third way is the shortest, only 17 km. 

But we will have to cross a river with no bridges. That will slow us down a lot, our speed will drop to 4 km/h." Talay said as they set off. 
 "Why don't you cast a little spell and fly us there?" said Beril. 
 "I lose energy after I cast a spell, and that wouldn't be a good idea, considering that my energy capacity decreases with every minute that passes. Then I would become a burden and slow you down even more. Besides, we don't know what awaits us there. I think I'llsave my magic for there," Talay said. 

"Then let's hurry and get to the cave as soon as possible," said Deniz. 

  "So, which way will we go?" asked Defne.

Cemre said, "If our goal is to get there as soon as possible, we need to make calculations. Our arrival time was the ratio of the speed of the road we were traveling, right? Then we need to ratio 24 to 6 on the first road, 19 to 5 on the second road and 17 to 4 on the third road." 
 "Then the first road takes 4 hours, but how do we compare the second and third roads?" asked Deniz. 
 Defne said, "We spend less than 4 hours on the second road. Because if the road was 20 km, we would travel at a speed of 5 km per hour in 4 hours, but the road is shorter than 20 km. So the time will be less." 
 

"With this logic, we will get the most time if we take the third road. Because if we travel at 4 km/h, we can go 16 km in 4 hours. However, the road is 17 km and longer. Then the time will be more." said Beril. 
 "Come on, let's take the second road then!" Cemre urged her friends. 

They had just started on the road, but they were already using math.

Chapter 3 - The Adventure Begins

Osama Abu Najili's Team

Al'imam Alshafie Primary School for Boys

Sahab/ Jordan

The friends started walking on the second road. The path was a bit bumpy, but they could walk quickly. Talay was accompanying them, but he looked very tired. The friends often gave him water and insisted that he rest. But Talay told them they had to hurry and gave them some information about the cave. "The cave is very dark and labyrinthine. It is possible that there are monsters and traps created by Abra's magic. We must avoid them while solving the riddles. The riddles are written on the walls of the cave and each time we solve a riddle a door will open. The doors will bring us closer to the dungeon." The friends listened carefully to all that was said and continued on their way with some anxiety, some fear but

determination.

After about three hours they reached the entrance to the cave. The cave was huge and dark. There was a large stone at the mouth of the cave. There was an inscription on the stone:

"Hello dear guests, how nice to see you here! But if you want to pass through here, you have to answer a question. 

Today at home, three cheese pies were baked on three equal trays for three siblings aged 4, 6 and 8. Each tray was divided into as many slices as the children were old enough to eat. Each sibling ate a slice from their own tray. Now tell me the fractions eaten, which siblingate the most?" 

Beril said, "So we are starting with this question, I hope the questions will always be like this." Defne said, "Yes, the younger brother's tray was divided into 4 slices, the middle brother's tray into 6 slices and the older brother's tray into 8 slices. 

They each ate one slice. Then the younger brother ate 1/4 of the tray, the middle brother ate 1/6 of the tray and the older brother ate 1/8 of the tray. In this case, the older brother ate the most. Don't the older ones always eat more?"

Cemre said, "No, Defne! You did very well until the end, but you gave the wrong answer. The youngest sibling must have eaten the most. Imagine, each tray is of equal size. Then you divide one of the trays into 4, the other into 6, and the other into 8. In this case, as the number of slices increases, the pies do not stay the same size. They all ate a slice, but the little brother had one slice bigger than the others."

"You're right, I missed it, I guess I couldn't pay attention because I was excited when the question was easy." Defne said and her other friends confirmed the answer. Then they repeated the correct answer to the stone and it moved with a great noise, giving way to Talay and the four friends.

Chapter 4 - The Secret Of The Passage

Haneen Majali's Team

Dmnh Mixed Elemantary School

Karak / Jordan

When Talay and his friends entered the cave, they first struggled with the darkness. But after a while their eyes adjusted and they began to explore the cave. Inside the cave, the sound of water was so faint that they could hear the flow of underground rivers. As they walked through the cave, they began to record their tracks so as not to lose their bearings.  After each intersection, they marked the path they took until the next intersection. As the cave deepened, it gradually became narrower. Finally, they came to a passage. In the center of the passage was a large block of stone. On the block was an inscription:

 "If you want to cross this pass, you must first know the

question. Four brothers raced along the road, one of 

them got here in 25.17 seconds, the others in 25,2; 25,175 and 25,34. Guess which brother got here first?"

Beril said, "That's simple too. They all started with 25 anyway, if we look at the decimal part after the comma,

there are 17, 2, 175 and 34. Since the smallest one is 2, the answer must be 25,2." 

Deniz stopped her: "But don't you think you overlooked this? You read and evaluated the decimals as natural numbers. However, one is 17 percent, one is 2 tenths, one is 175 per thousand, and the other is 34 percent.

"Oh, you're right." said Beril, "I would have noticed if I had even gotten the pronunciation right. This is all due 

to excitement! So how are we going to sort them now?"

"By adding zeros at the end of the numbers, we can make them all in thousand, like an expansion. Instead of 17 percent it's 170 per thousand, instead of 2 tenths it's 200 per thousand, instead of 34 percent it's 340 per thousand. 

The other one was already 175 per thousand. Thus, they all have a denominator of 1000. And if we rank them according to their shares, the smallest one was 170 per thousand. So the one who completed the race in 25,17 seconds won." said Deniz. 

When all four friends confirmed the answer, they turned and said it towards the stone block. The stone block moved and turned into a bridge for the four friends to 

cross the passage.

Chapter 5 - Mathematical Mysteries

Filiz İşlek's Team

Mehmet Ahmet Genç Secondary School

Gönen / Balıkesir

After passing through the passage, Talay and his friends reached a deeper part of the cave. Here they saw various paintings and writings on the cave walls. 

Talay said that they belonged to an ancient civilization. In this civilization, mathematics was very advanced and they used fractions very well. 

Talay said, "These paintings and writings can give us clues. Maybe we should look at them to solve riddles." When the friends looked closely at the walls, they saw various symbols representing fractions. For example, there was a symbol with two dots in a circle. Talay said this meant half. There was also a symbol with three dots inside a triangle. This meant one third. Then suddenly the path ended and there was a wall and a fraction on it. In the numerator there were five dots inside a pentagon and in the denominator there were six dots inside a hexagon. Nothing else was written. 

Defne said, "What are we going to do now? The road is over and there is no riddle!" she said in a worried voice. 
 Beril said, "Did you take us the wrong way? And when time is so precious." Beril lashed out at Talay. 
 "Girls, calm down!" said Cemre. "Maybe this is a new riddle. If we consider the other symbols and the pattern in the symbols, a pentagon with five dots in it would be 1/5 at best. A hexagon with six dots would be 1/6. We remember that the fraction line can be used instead ofdivision, right? So the answer to our riddle here is 1/5 divided by 1/6. Let's do it now!" 

Defne said excitedly, "When we were doing division with 

fractions, we were writing the divisor exactly and multiplying it by the inverse of the divisor according to the multiplication." 

Beril said, "You can call it writing the first fraction exactly and multiplying the second fraction upside down." They laughed, teasing Defne.

Cemre said, "Then let's do 1/5 times 6/1. We multiply the numerator by the numerator and write it in the numerator, and multiply the denominator by the denominator and write it in the denominator. Then the answer is 6/5!" When everyone agreed, they chanted the answer towards the wall. The wall suddenly disappeared as if it had never been there and the road opened up.

Chapter 6 - The Threat of The Cyclops

Berna Tunca Eygül's Team

Atatürk Secondary School

Pehlivanköy / Kırklareli

"We are almost halfway there and fortunately the questions didn't push us too hard," said Beril. The group was now walking more confidently and enjoying the work. Talay said, "Once again, thank you very much for your help. But I must warn you about Abra's monsters. If we give the wrong answer, we will be in big trouble," Talay warned his friends. He had just finished when a monster with a center eye bigger than the other two leapt out at them. The monster spoke slowly in a thick voice: "Hold on, travelers, you want to move forward, here is a question for you: Out of my 20 children, the ratio of my sons to my daughters is 2/3, this is a very difficult question to solve.

 My blond sons are three quarters of all my sons, now tell me how many blond sons do I have? If you can answer the question, all the better, but if you can't, then you are my children's dinner."

The children had never imagined that one day they would come face to face with this creature they knew from stories and mythologies. Moreover, the monster threatened them. 

Despite all this pressure, Cemre stepped forward and shouted at the monster: "Of course we will solve this question and you will get out of our way!" Then she turned to her friends: "Girls, we will solve this question. Let's get started. The ratio of the monster's sons to his daughters is 2/3. Then he had 3 daughters for every 2 sons. In that case, he would have 5 children. But he had 20 children, which means there are 4 groups of 5 children. Since he has 2 sons in each group, he has 4x2=8 sons in total." 

Deniz said, "You are right. Now let's find the blond ones. Three fourths of the 8 sons were blond. So when we divide 8 people into four groups, everyone in 3 of 

these groups will be blonde. So let's divide the 8 into groups of four, each group will have 2 people. Everyone in three of these groups was blonde. Then 2x3=6 boys will be blonde!" she said excitedly. When Defne and Beril approved the solutions, they each said the answer as if they were a victorious commander and watched the monster move out of their way.

Chapter 7 - Meet Arçuri

Tuğçe Aydın's Team

Atatürk Secondary School

Ondokuzmayıs / Samsun

As the monster slowly retreated, the friends hugged each other with joy. "You guys are great!" said Cemre, "But I think we are ready to solve more riddles. This adventure is far from over." The others joined her and continued on their way.

After a while, they came upon a dark-looking thing with hair sweeping the floor and a body covered in bristles. Talay recognized it immediately. This little forest goblin was Archuri and one of Abra's servants. He immediately told the girls about it. 

Archuri had already approached them and started talking: "Stop, travelers, where are you going? It is not easy to go. First know this question, then go the way you

want. After completing a third of a job, I worked at the same pace for 6 more days and finished a quarter of the remaining work. At the same pace, how many days did I finish the entire job?"

Beril said, "It seemed complicated to me when I read it poetically, what is he asking now?" Defne said, "Actually, it is not difficult, but you need to go step by step.

 After working for 6 days, we need to find out how much of the work he finished. First, he finished 1/3 of the work, but it is not clear how many days. Then he finished 1/4 of the remaining work, i.e. 2/3 of it, in a total of 6 days. This is the knot. We have to find out how many times 1/4 of 2/3 of the work is." 

Cemre and Deniz were listening to their friends and checking their work. Defne continued: "The 1/4 of 2/3 was found by multiplying these two fractions. When multiplying fractions, we multiply the numerator by the numerator and write it in the numerator, and multiply the denominator by the denominator and write it in the denominator. Then the product will be 2/12. 

So he actually finished 2/12 of the work in 6 hours."

"Then, if he did a job in 12 parts, that means he finished two parts in 6 hours." Beril interjected excitedly. "Well, then he could do one piece in 3 hours and 12 pieces in 36 hours!" she said, applauding herself and her friends and hugging Defne. When Cemre and Deniz agreed, they told

the answer to Archuri. When Archuri heard the answer, he stepped aside and gave way to his friends.

Chapter 8 - Invisible Labyrinth

Gülünaz Tozlu's Team

Kumcığaz Secondary School

Terme / Samsun

As they continued walking, Cemre suddenly realized that they were walking around the same place. The marks they had drawn on the wall to keep their bearings were repeating. She immediately warned her friends: "Hey, I think we've started to wander around the same place. Look, here are the marks we made before. Could there be another passage hidden here? Talay, you were talking about the maze." 

Talay said, "Yes, you're right, it could be! Let's look around carefully. Maybe there is a sign on the walls." 

Just at that moment, Deniz realized something else. The fraction 2/5 was written on the wall. When she ran her hand over the fraction, they saw that the road in front of them became transparent and divided into three. 

"Well, where should we go now?" said Deniz, "Let's examine the walls again and go in the right direction, we've already lost a lot of time."