# data[].attributes.headline
Please introduce yourselves. Name, age, institution...

# data[].attributes.subject
Please introduce yourselves. Name, age, institution...

# data[].attributes.headline
Write down the ideas and progress of your group on your topic

# data[].attributes.subject
Write down the ideas and progress of your group on your topic

# data[].attributes.body
Hi! My name is Alice and I'm in 11th grade (i'm 16 years old) in Pertuis. I went to Satu Mare and Cluj and I can't wait to see some of you in April :)
Good luck with your research !

PS: Hello to those who were at one of the two trips !

# data[].attributes.body
Hello everyone!
My name is Léni and I am 15 years old.
I'm at the "Val de Durance" high school in Pertuis.
I have already met some of you in Romania.
I hope that our exchanges will allow us to move forward more quickly.
Good work!

# data[].attributes.body
Hi, my name is Petra and I am 15 years old.
I study at National College "Emil Racovita" in Cluj.
I'm looking forward to meeting you and discussing our approaches on the MaSud topic! :)
Good luck with your research !

# data[].attributes.body
Hello!
Today, I told my group what we did when I was in Romania with some of you about the subject. My french friends and me decided to think about how many plays needs the machine to be able to win everytime and make sure that this number would be right and relieable.

Alice (working with Alexandre, Aurélie, Lili and Gaël sometimes)

# data[].attributes.body
Hello, i am Lili and i am 15 years old. I am a student in Val de Durance highschool. I am glad to work with you and i hope we'll make a great math project.
Good luck ^^

# data[].attributes.body
Hello, My name is Théo, I'm 15 years old and I'm a student in Lycée Val de Durance.
It's amazing to work and share our exeperience and ideas on the stick game topic with you.
Good luck and hope chat with you soon.

# data[].attributes.body
Hi ! My name is Lucas , I'm 15 years old and I'm a student in the Val de Durance  high school.
I am pround to share this project with you.
I wish you a good luck with your reshearch ! :)

# data[].attributes.body
Hi !
I'm Joée, I'm 15 yo and I'm studying in Val de Durance hight school in Pertuis.
I look forward to working with all of you and share our work !
Good luck with your research :)

# data[].attributes.body
Hi!
Today we have worked on the first question wich is "How many plays needs the machine to be able to win".
Our first idea is to make an average of the numbers of plays that the machine takes for always win.

Lucas , Théo , Joée
Val de Durance High School

# data[].attributes.body
Hi ! My name is Clément, I'm 17yo and I'm a student from the high school val de durance in Pertuis, in the south of the France !
I'm really exited to work with you and I hope you good luck !
See you soon

# data[].attributes.body
Hello my name is Louis, I'm 16 yo and I'm studying at Val de Durance in Pertuis.
I'm really interested to work on the project with you ! Good Luck
See you soon !

# data[].attributes.body
Hello, my name is Idrisse, I'm 17 and I study in Val de Durance.
I like programming and taking math for fun.
I wish we will do a great work around this subject!
Good luck and have fun

# data[].attributes.body
Hi !
My name is Jules and I am 15 years old. I'm a student from " Val de Durance" high school in Pertuis.
I look forward to working with you and share our work!
Good luck for the topic !

# data[].attributes.body
Hello, my name is Oscar and I am 15 years old. I'm a studying at Val de Durance in Pertuis. I'm looking forward to working with you and I hope we will make a good math project !
Good luck for the topic !

# data[].attributes.body
We have an idea to answer your question.
In Romania, we have been thinking about the minimum number of strokes to stabilise the machine.
We think that this number is 13, according to the following criteria:
-There are 8 cups
-We can remove one or two sticks per stroke
-The human plays with the winning strategy
We agree that this number is 13 but we can't prove it.
If you can, please tell us.

It is difficult to give an average number of moves to stabilise the machine as there will be extremely high values.

Jules, Oscar, Titouan, Arthur et Léni ( Val de Durance high school)

# data[].attributes.body
Hey !
My name is Arthur and I'm 15 years old.
I'm studying at the "Val de Durance" highschool in Pertuis.
I really hope that our exchanges will make glow up the project
Anyway, good work, good luck and great experimantations ;)
Arthur

# data[].attributes.body
Hello, I am Titouanos and I am 15 yaers old .
I'm a studying at Val de Durance in Pertuis in France.
I'm looking forward to working with you and I hope we will make a good math project !!!
Above all, stay motivated !!!

# data[].attributes.body
Hi, my name is Petru and I study at National College Emil Racoviță in eleventh grade, in Cluj-Napoca. I like programming and mathematics. I hope to solve this problem together. Good luck!

# data[].attributes.body
Hello guys ! My name is Aurélie, I'm 16 years old and I study in Val de Durance highschool.
I'm glad to work with you, and I'm looking forward to team up with you on our math project.
Good luck everyone :)

# data[].attributes.body
Hi, my name's Alyssa, i'm 15, my high school is Bellevue, in Ales. I'm really looking forward to finally solve this problem !

# data[].attributes.body
Hello everybody !! I am sarah from bellevue marie rivier in ales. I’m 15 years old. 👍

# data[].attributes.body
Hi !
So, when we first started to work on this subject, we draw a probability tree, so that we could have all the ways that the machine has to win. However, nothing concrete came out of it, so we decided to put it aside and focus on writing an algorithme in Python, that would represent a game between the machine and the player (but we're not finished yet, we need to add the cups on the programm ). We did this, so that we could play with it over and over and then find a winning combination that would repeat itself. Conversly, we're still stuck at the player issue : since it decides its moves, there's no way that a combination could repeat itself, because the player would make sure that it wouldn't🤷‍♀️.
Plus, we dont really understand how you found 13 :(
Do you have any thoughts or ideas about this ?
Alyssa, Sarah and Jeanne

# data[].attributes.body
hey guys !
My name is Jeanne and I am one of the student that is working together with you on this project !
I am a student in Bellevue (Alès)
And I'm in year eleven.
I'm looking forward to working with you, and good job everyone !

# data[].attributes.body
Hi!
First, for the human player question:
In our calculations, we play the human with the winning strategy:
This is a strategy that consists of making blocks of n+1 cups, where n represents the number of colors. The goal to win is to make the machine start its packs and whatever its game, the human can finish its packs. He will then finish the game and win.
Second, for the number 13 question:
-There are only 4 of the 8 cups to stabilize: the 2,4,5 and 8
-In each cup to be stabilized there are two sticks to remove:
2 yellow in the 8, 2 yellow in the 5, 2 red in the 4 and 2 yellow in the 2.
-So there are already 8 rounds necessary to stabilize these 4 cups. But by making the machine lose 2 times we remove the yellows in the 8. During the next 2 turns to stabilize the 5, we also remove the 2 reds from the 8, so we have to put 2 reds and 2 yellows in the 8. This action then requires two new turns to remove the 2 new yellows. The same thing happens for the cups 4 and 2. This gives the number 14. But by making the machine win one turn before losing it, we avoid emptying the cup 8 and we therefore win one turn. This gives 13.
I hope you have understood.
If you work on this question and find a way to prove this number, please share your reasoning.
Good luck to you
Arthur, Titouan, Oscar, Jules and Léni

# data[].attributes.body
Hi there,
We are moving slowly but surely in the project. The question we asked ourselves is how many turns the machine reaches an optimal configuration to constantly win, and to solve this question, we have the right to choose how the player will play.
We have begun to answer this question and we will keep you informed of our progress. Have a good day and good research.
Théo, Lucas and Joée

# data[].attributes.body
Hey!
Today, we worked on the question we asked ourselves last week, which is: "Find an optimal configuration for the machine to win at each turns, how many turns at least it takes to reach this configuration knowing that the player does not have a winning strategy (he plays optimally). The optimal configuration we found is: n red brick in 1 glass, base brick in 2 and 3, n red brick in 4, n yellow brick in 5, base brick in 6, n red brick in 7 and base brick (yellow) for 8. ( n is a number greater than 1, the number of red brick does not matter as long as it is greater than 1, base bricks means that the color and number of bricks in the glasses does not matter).
Théo, Lucas and Joée

# data[].attributes.body
After finding this optimal configuration, we looked for how many turns it takes at least for the machine to reach the configuration seen above and win with each test.
We found that it takes at least 5 turns for the machine to reach this configuration. The machine has to lose its red bricks in glasses 1,4 and 7. Once it has lost them, it has to win 1 red brick in the glass to be able to lose its two red bricks in vere 5.
After that, we reach the optimal confguration we found and the machine wins at every turn.
Goodbye and good research
Théo, Lucas and Joée

# data[].attributes.body
Hello,
My name is Louis, I'm 16 and I study in Val de Durance. I like playing music, reading, and obsviously making math!
I wish we will do a great work together!
See you soon

# data[].attributes.body
Presentation to an Italian delegation from a Palermo institution
https://www.lyc-valdedurance.ac-aix-marseille.fr/spip/spip.php?article3112

# data[].attributes.body
Hey!
These past few weeks we’ve been working on developing a C++ program which answers the first question of the research topic: “On average, how many games does it take for the machine to always win?”. We made the machine play until it always won 50000 times. Then, we calculated the average between the number of games after which it always won and the result was around 157.

While implementing this program, we realized that if the player’s moves are random, the machine cannot learn from them. So we came up with the best strategy for the player
(we represent each ball with the number of sticks it removes and 0 if it’s the machine’s turn):  {1, 2, 0, 1, 2, 0, 1, 2}
cup 1: 1, cup 2: 2, cup 3: 0, cup 4: 1, cup 5: 2, cup 6: 0, cup 7: 1, cup 8: 2

Good luck to everyone!
Petra, Matei, Stefan

# data[].attributes.body
Hi and Happy new year !
We worked on the question : " How many turns at least it takes to reach this configuration ". We found 5 turns too. Upper, here is the demonstration.
Jules, Arthur, Titouanos, Oscar and Léni

# data[].attributes.body
Hello, my name is George and I am 16 years of age. I am currently studying at National College "Emil Racovita" in Cluj and I look forward to the day we will be discussing our approaches related to the topic.

# data[].attributes.body
Hey!

We generalized our C++ program which determines after how many games the machine always wins. Now, we can find the answer for any number of cups, but we have a particular case. Our player has the optimal strategy: j[] = {1, 2, 0, 1, 2, 0, ...} (1 - one stick removed, 2 - two sticks removed, 0 - removes a random number of sticks between 1 and 2). If the number of cups is a multiple of 3, the machine will never always win, because it starts from the position where the player's strategy is j[n] = 0 and wins against the machine.

Petra, Matei, Stefan

# data[].attributes.body
Hi, my name is Matei Coldea and I am 17 years old. I am a student at Colegiul National "Emil Racovita" in Cluj-Napoca. I am very excited to work together with you, to find a solution to this problem!

# data[].attributes.headline
Video conference Wednesday, February 1 from 1:00 pm to 3:00 pm (French time)

# data[].attributes.subject
Video conference Wednesday, February 1 from 1:00 pm to 3:00 pm (French time)

# data[].attributes.body
Each group to present a small slide show on their research

# data[].attributes.body
Informatics approach:
We started by developing a c++ program that simulates the game.
After determining the optimal moves for the machine, we integrated it into the informatics module through randomness.
Using this program we guided our further research.

George, Petru, Matei

# data[].attributes.body
During the research for an idea to help with the generalization for the original problem (for a different n, where n is the number of cups and stiks) we came up with a few different mathematical approaches, that we will structure in a separate message for each approach.

Petru, Matei, George

# data[].attributes.body
Informatics approach #2:
We developed a binary tree, that simulates all the possible moves that either the man and the machine can make at any given moment.
On this tree we ran the minimax algorithm and determined for any given parameter for the problem, the optimal moves for the machine and the man at any given time and whether the situation is winnable by the machine or not.
We improved our algorithm a little further by applying alfa-beta pruning on the existing algorithm. This improvement allowed us to search deeper into the tree and approach cases that involve a high game tree depth.

George, Petru, Matei

# data[].attributes.body
The main idea on which each of these mathematical interpretations are built on is the use of a graph. The aforementioned graph contains a few points (xi, yi), x-the number n, y-the average number of games played before the machine always wins. We will try to create a function that characterizes each of these cases. We first used matrices to find the function, but this approach doesn't leave room for the error caused by the probabilities. This approach works best with the help of a program that generates the x and y values then finds out the function with the help of determinants. For t pairs (x,y) the program will generate a polynomial with the degree t-1.

Matei, Petru, George

# data[].attributes.body
Informatics approach #3:
We used the Monte Carlo algorithm to determine the approximate value of the number of rounds it takes the machine to always win.
Making use of the optimal path for the man and the machine, determined with the algorithm described in approach #2, we made a c++ program that runs for any given parameter and returns the mean value of the number of times it takes for the machine to always win.

George, Petru, Matei

# data[].attributes.body
Probabilistic approach:
Making use of the data that we determined using the Monte Carlo algorithm we determined the probability for the machine to always win after x rounds, using the Poisson distribution.
We calculated the mean value of unhelpful balls in cups after x rounds using the Monte Carlo algorithm and then we calculated using the distribution the probability.

George, Petru, Matei

# data[].attributes.body
Mathematical approach:
We developed a recursion formula for smaller parameters.
starting from the case of two sticks, two cups we went on to develop recursions until the case with five sticks , five cups.
This recursions were also implemented in c++ and were used to determine the number of games it takes for the machine to always win, under the given conditions.

George, Petru, Matei

# data[].attributes.headline
Another approach: the least squares regression line

# data[].attributes.subject
Another approach: the least squares regression line

# data[].attributes.body
This approach give a approximative line that represents the function on the graph, with a error due to the method used. This method enables us to calculate the function more easily but with a greater error. In this case, considering that the problem allows error, this method we will consider viable for a bigger n.

Petru, Matei, George

# data[].attributes.body
Presentation to the Val de Durance High School researcher.
Yves PAPEGAY - INRIA Sophia Antipolis

# data[].attributes.body
https://www.lyc-valdedurance.ac-aix-marseille.fr/spip/spip.php?article3136

# data[].attributes.headline
The video-conference (@Colegiul National Emil Racovita)

# data[].attributes.subject
The video-conference (@Colegiul National Emil Racovita)

# data[].attributes.headline
The video-conference - the 10th graders group from CNER

# data[].attributes.subject
The video-conference - the 10th graders group from CNER

# data[].attributes.headline
The video-conference - the 11th graders group from CNER

# data[].attributes.subject
The video-conference - the 11th graders group from CNER

# data[].attributes.headline
Elements to build the common presentation during the congress in Nice

# data[].attributes.subject
Elements to build the common presentation during the congress in Nice

# data[].attributes.body
Hello! We made a few slides for the presentation. Feel free to complete it.

# data[].attributes.headline
Presentations in Pertuis secondary schools

# data[].attributes.subject
Presentations in Pertuis secondary schools

# data[].attributes.body
Presentations in Pertuis secondary schools https://www.site.ac-aix-marseille.fr/lyc-valdedurance/spip/Presentations-aux-collegiens-de-Marcel-Pagnol.html and https://www.site.ac-aix-marseille.fr/lyc-valdedurance/spip/Presentations-au-college-Marie-Mauron.html

# data[].attributes.headline
Topic 1 @ the National Olympiad of Scientific Creativity (Cluj county) - 27 April 2023

# data[].attributes.subject
Topic 1 @ the National Olympiad of Scientific Creativity (Cluj county) - 27 April 2023

# data[].attributes.body
Presentation of the research topic 1-The machine to play the sticks game & its research results at the (Cluj) county level of the National Olympiad of Scientific Creativity. The students' presentation qualified for the national level of this olympiad.

# data[].attributes.body
MaSuD at the Faites de la science competition at the Faculté St Jérôme in Marseille
https://www.site.ac-aix-marseille.fr/lyc-valdedurance/spip/ERASMUS-MaSuD-au-concours-Faites-de-la-science.html

# data[].attributes.body
Slide presentation at the MATh.en.JEANS Congress in Nice

# data[].attributes.headline
Topic 1 @ the National Olympiad of Scientific Creativity (national level) - Suceava University 5-9 July 2023

# data[].attributes.subject
Topic 1 @ the National Olympiad of Scientific Creativity (national level) - Suceava University 5-9 July 2023

# data[].attributes.body
Petra Hedeșiu & Matei Bojan presented the research topic & their findings at the national level of the National Olympiad of Scientific Creativity. They were rewarded with the Suceava University honorable mention prize.

# data[].attributes.attachment_link.title
Article - The machine to play the sticks game