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      <title>1.The machine to play the sticks game by </title>
      <link>https://padlet.com/proalh/isd27i55rpj2tlf8</link>
      <description>Threads of discussion between MaSuD 2022-2023 students of topic n°1</description>
      <language>en-us</language>
      <pubDate>2022-11-01 09:37:47 UTC</pubDate>
      <lastBuildDate>2023-07-20 20:28:09 UTC</lastBuildDate>
      <webMaster>hello@padlet.com</webMaster>
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      <item>
         <title>Please introduce yourselves. Name, age, institution...</title>
         <author>proalh</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2364666050</link>
         <description><![CDATA[]]></description>
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         <pubDate>2022-11-01 09:50:41 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2364666050</guid>
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      <item>
         <title>Write down the ideas and progress of your group on your topic</title>
         <author>proalh</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2364668133</link>
         <description><![CDATA[]]></description>
         <enclosure url="" />
         <pubDate>2022-11-01 09:53:09 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2364668133</guid>
      </item>
      <item>
         <title>Alice ROBIN</title>
         <author>estellealicepierre</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2369068757</link>
         <description><![CDATA[<div>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 :)<br>Good luck with your research&nbsp;!<br><br>PS: Hello to those who were at one of the two trips !</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-03 19:52:48 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2369068757</guid>
      </item>
      <item>
         <title>Léni FANJAUD</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2373625413</link>
         <description><![CDATA[<div>Hello everyone!<br>My name is Léni and I am 15 years old.<br>I'm at the "Val de Durance" high school in Pertuis.<br>I have already met some of you in Romania.<br>I hope that our exchanges will allow us to move forward more quickly.<br>Good work!</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-07 18:27:20 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2373625413</guid>
      </item>
      <item>
         <title>Petra Hedesiu</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2376702433</link>
         <description><![CDATA[<div>Hi, my name is Petra and I am 15 years old.<br>I study at National College "Emil Racovita" in Cluj.&nbsp;<br>I'm looking forward to meeting you and discussing our approaches on the MaSud topic! :)<br>Good luck with your research !<br><br></div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-09 12:25:44 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2376702433</guid>
      </item>
      <item>
         <title>15/11/22</title>
         <author>estellealicepierre</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2384733378</link>
         <description><![CDATA[<div>Hello!<br>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.<br><br>Alice (working with Alexandre, Aurélie, Lili and Gaël sometimes)</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-15 12:49:02 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2384733378</guid>
      </item>
      <item>
         <title>Lili Mengin</title>
         <author>estellealicepierre</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2384750508</link>
         <description><![CDATA[<div>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.<br>Good luck ^^</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-15 13:01:46 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2384750508</guid>
      </item>
      <item>
         <title>Cincotta Théo </title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2387919632</link>
         <description><![CDATA[<div>Hello, My name is Théo, I'm 15 years old and I'm a student in Lycée Val de Durance.<br>It's amazing to work and share our exeperience and ideas on the stick game topic with you.<br>Good luck and hope chat with you soon.</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-17 08:34:12 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2387919632</guid>
      </item>
      <item>
         <title>Cincotta Lucas</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2387921084</link>
         <description><![CDATA[<div>Hi ! My name is Lucas , I'm 15 years old and I'm a student in the Val de Durance&nbsp; high school.<br>I am pround to share this project with you.<br>I wish you a good luck with your reshearch ! :)<br><br></div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-17 08:35:34 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2387921084</guid>
      </item>
      <item>
         <title>Joée BUET-PES</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2387925731</link>
         <description><![CDATA[<div>Hi !<br>I'm Joée, I'm 15 yo and I'm studying in Val de Durance hight school in Pertuis.<br>I look forward to working with all of you and share our work !<br>Good luck with your research :)<br><br></div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-17 08:39:55 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2387925731</guid>
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      <item>
         <title>17/11/22</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2387940596</link>
         <description><![CDATA[<div>Hi!<br>Today we have worked on the first question wich is "How many plays needs the machine to be able to win".<br>Our first idea is to make an average of the numbers of plays that the machine takes for always win.<br><br>Lucas , Théo , Joée<br>Val de Durance High School</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-17 08:53:55 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2387940596</guid>
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      <item>
         <title>Helloooo</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2388135759</link>
         <description><![CDATA[<div>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 !<br>I'm really exited to work with you and I hope you good luck !<br>See you soon </div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-17 11:45:59 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2388135759</guid>
      </item>
      <item>
         <title>D&#39;or est le nueve</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2388151667</link>
         <description><![CDATA[<div>Hello my name is Louis, I'm 16 yo and I'm studying at Val de Durance in Pertuis.<br>I'm really interested to work on the project with you ! Good Luck<br>See you soon !</div>]]></description>
         <enclosure url="https://www.trollfootball.me/upload/full/2019/04/21/karim-benzema-deserves-the-ballon-d.jpg" />
         <pubDate>2022-11-17 12:00:34 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2388151667</guid>
      </item>
      <item>
         <title>Idrisse Ibrahim</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2388274888</link>
         <description><![CDATA[<div>Hello, my name is Idrisse, I'm 17 and I study in Val de Durance.&nbsp;<br>I like programming and taking math for fun.<br>I wish we will do a great work around this subject!<br>Good luck and have fun</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-17 13:32:17 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2388274888</guid>
      </item>
      <item>
         <title>Jules Couturier </title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2390473275</link>
         <description><![CDATA[<div>Hi !&nbsp;<br>My name is Jules and I am 15 years old. I'm a student from " Val de Durance" high school in Pertuis.<br>&nbsp;I look forward to working with you and share our work!&nbsp;<br>Good luck for the topic !&nbsp;</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-18 21:19:29 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2390473275</guid>
      </item>
      <item>
         <title>Oscar Brunooghe</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2392516786</link>
         <description><![CDATA[<div><mark>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 !&nbsp;<br>Good luck for the topic !</mark></div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-21 12:21:12 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2392516786</guid>
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      <item>
         <title>21/11/22</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2392520129</link>
         <description><![CDATA[<div><mark>We have an idea to answer your question.<br>In Romania, we have been thinking about the minimum number of strokes to stabilise the machine.<br>We think that this number is 13, according to the following criteria:<br>-There are 8 cups<br>-We can remove one or two sticks per stroke<br>-The human plays with the winning strategy<br>We agree that this number is 13 but we can't prove it.<br>If you can, please tell us.<br><br>It is difficult to give an average number of moves to stabilise the machine as there will be extremely high values.<br><br></mark>Jules, Oscar, Titouan, Arthur et Léni ( Val de Durance high school)</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-21 12:24:14 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2392520129</guid>
      </item>
      <item>
         <title>Arthur VAYRON</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2392531339</link>
         <description><![CDATA[<div>Hey !<br>My name is Arthur and I'm 15 years old.<br>I'm studying at the "Val de Durance" highschool in Pertuis.<br>I really hope that our exchanges will make glow up the project<br>Anyway, good work, good luck and great experimantations ;)<br>Arthur&nbsp;</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-21 12:34:28 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2392531339</guid>
      </item>
      <item>
         <title>Titouan Foissy</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2392557183</link>
         <description><![CDATA[<div>Hello, I am Titouanos and I am 15 yaers old .<br>I'm a studying at Val de Durance in Pertuis in France.<br>I'm looking forward to working with you and I hope we will make a good math project !!!<br>Above all, stay motivated !!! &nbsp;</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-21 12:56:15 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2392557183</guid>
      </item>
      <item>
         <title>Pentru Săveanu </title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2393113407</link>
         <description><![CDATA[<div>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!</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-21 19:46:59 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2393113407</guid>
      </item>
      <item>
         <title>Aurélie FERU</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2393129960</link>
         <description><![CDATA[<div>Hello guys ! My name is Aurélie, I'm 16 years old and I study in Val de Durance highschool.&nbsp;<br>I'm glad to work with you, and I'm looking forward to team up with you on our math project.<br>Good luck everyone :)</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-11-21 20:04:40 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2393129960</guid>
      </item>
      <item>
         <title>Alyssa ANDRES</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2408972730</link>
         <description><![CDATA[<div>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 !   </div>]]></description>
         <enclosure url="" />
         <pubDate>2022-12-05 11:30:59 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2408972730</guid>
      </item>
      <item>
         <title>Sarah ZOUAD </title>
         <author>sarahitme8</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2408987392</link>
         <description><![CDATA[<div>Hello everybody !! I am sarah from bellevue marie rivier in ales. I’m 15 years old. 👍</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-12-05 11:45:55 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2408987392</guid>
      </item>
      <item>
         <title>Updates from Ales</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2409021591</link>
         <description><![CDATA[<div>Hi !&nbsp;<br>&nbsp;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🤷‍♀️.<br>Plus, we dont really understand how you found 13 :(<br>Do you have any thoughts or ideas about this ?<br>&nbsp;Alyssa, Sarah and Jeanne </div>]]></description>
         <enclosure url="" />
         <pubDate>2022-12-05 12:20:14 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2409021591</guid>
      </item>
      <item>
         <title>Jeanne Siboulet</title>
         <author>jeannesiboulet76</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2409338519</link>
         <description><![CDATA[<div>hey guys !&nbsp;<br>My name is Jeanne and I am one of the student that is working together with you on this project !<br>I am a student in Bellevue (Alès)&nbsp;<br>And I'm in year eleven.&nbsp;<br>I'm looking forward to working with you, and good job everyone !</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-12-05 15:45:02 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2409338519</guid>
      </item>
      <item>
         <title>12-12-2022</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2417698523</link>
         <description><![CDATA[<div>Hi!<br>First, for the human player question:<br>In our calculations, we play the human with the winning strategy:<br>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.<br>Second, for the number 13 question:<br>-There are only 4 of the 8 cups to stabilize: the 2,4,5 and 8<br>-In each cup to be stabilized there are two sticks to remove:<br>2 yellow in the 8, 2 yellow in the 5, 2 red in the 4 and 2 yellow in the 2.<br>-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.<br>I hope you have understood.<br>If you work on this question and find a way to prove this number, please share your reasoning.<br>Good luck to you<br>Arthur, Titouan, Oscar, Jules and Léni</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-12-12 12:42:21 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2417698523</guid>
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      <item>
         <title>Update 08/12/22</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2421450514</link>
         <description><![CDATA[<div>Hi there,<br>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.<br>We have begun to answer this question and we will keep you informed of our progress. Have a good day and good research.&nbsp;<br>Théo, Lucas and Joée</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-12-15 05:48:22 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2421450514</guid>
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      <item>
         <title>Update 15/12/22</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2421581082</link>
         <description><![CDATA[<div>Hey!&nbsp;<br>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).<br>Théo, Lucas and Joée</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-12-15 08:50:41 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2421581082</guid>
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      <item>
         <title>Update 15/12/22 (suite)</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2421586415</link>
         <description><![CDATA[<div>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.<br>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.<br>After that, we reach the optimal confguration we found and the machine wins at every turn.<br>Goodbye and good research<br>Théo, Lucas and Joée</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-12-15 08:56:52 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2421586415</guid>
      </item>
      <item>
         <title>Louis PACCOUD</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2421811695</link>
         <description><![CDATA[<div>Hello,<br>My name is Louis, I'm 16 and I study in Val de Durance. I like playing music, reading, and obsviously making math!<br>I wish we will do a great work together!<br>See you soon</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-12-15 13:14:44 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2421811695</guid>
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      <item>
         <title>13/12/2022</title>
         <author>proalh</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2425637478</link>
         <description><![CDATA[<div>Presentation to an Italian delegation from a Palermo institution<br>https://www.lyc-valdedurance.ac-aix-marseille.fr/spip/spip.php?article3112</div>]]></description>
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         <pubDate>2022-12-20 10:00:31 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2425637478</guid>
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      <item>
         <title>update 21/12/2022</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2428388051</link>
         <description><![CDATA[<div>Hey!<br>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.<br><br>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<br>(we represent each ball with the number of sticks it removes and 0 if it’s the machine’s turn):&nbsp; {1, 2, 0, 1, 2, 0, 1, 2}<br>cup 1: 1, cup 2: 2, cup 3: 0, cup 4: 1, cup 5: 2, cup 6: 0, cup 7: 1, cup 8: 2<br><br>Good luck to everyone!<br>Petra, Matei, Stefan</div>]]></description>
         <enclosure url="" />
         <pubDate>2022-12-24 19:32:31 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2428388051</guid>
      </item>
      <item>
         <title>09/01/2023</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2437715159</link>
         <description><![CDATA[<div>Hi and Happy new year !<br>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.<br>Jules, Arthur, Titouanos, Oscar and Léni&nbsp;<br><br></div>]]></description>
         <enclosure url="https://padlet-uploads.storage.googleapis.com/1929917097/b4d13bd263953b25130c6a53dbd822d3/MeJ_stabmach.odt" />
         <pubDate>2023-01-09 13:03:48 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2437715159</guid>
      </item>
      <item>
         <title>George Iorga</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2456683555</link>
         <description><![CDATA[<div>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.</div>]]></description>
         <enclosure url="" />
         <pubDate>2023-01-25 19:23:17 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2456683555</guid>
      </item>
      <item>
         <title>update 25/01/2023</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2457891105</link>
         <description><![CDATA[<div>Hey!</div><div>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.<br><br>Petra, Matei, Stefan</div><div><br><br></div>]]></description>
         <enclosure url="" />
         <pubDate>2023-01-26 16:46:24 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2457891105</guid>
      </item>
      <item>
         <title>Matei Coldea</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2459995178</link>
         <description><![CDATA[<div>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!</div>]]></description>
         <enclosure url="" />
         <pubDate>2023-01-28 21:21:29 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2459995178</guid>
      </item>
      <item>
         <title>Video conference Wednesday, February 1 from 1:00 pm to 3:00 pm (French time)</title>
         <author>proalh</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460001078</link>
         <description><![CDATA[<div>Each group to present a small slide show on their research&nbsp;</div>]]></description>
         <enclosure url="" />
         <pubDate>2023-01-28 21:40:33 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460001078</guid>
      </item>
      <item>
         <title>Updates from Cluj-Napoca</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460361354</link>
         <description><![CDATA[<div>Informatics approach:<br>&nbsp;We started by developing a c++ program that simulates the game.<br>&nbsp;After determining the optimal moves for the machine, we integrated it into the informatics module through randomness.<br>&nbsp;Using this program we guided our further research.<br><br>George, Petru, Matei</div>]]></description>
         <enclosure url="" />
         <pubDate>2023-01-29 15:31:42 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460361354</guid>
      </item>
      <item>
         <title>Update From Cluj-Napoca</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460362717</link>
         <description><![CDATA[<div>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 <strong>mathematical</strong> approaches, that we will structure in a separate message for each approach.<br><br>Petru, Matei, George</div>]]></description>
         <enclosure url="" />
         <pubDate>2023-01-29 15:34:13 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460362717</guid>
      </item>
      <item>
         <title>Updates from Cluj-Napoca</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460367082</link>
         <description><![CDATA[<div>Informatics approach #2:<br>We developed a binary tree, that simulates all the possible moves that either the man and the machine can make at any given moment. &nbsp;<br>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.<br>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.<br><br>George, Petru, Matei<br><br></div>]]></description>
         <enclosure url="" />
         <pubDate>2023-01-29 15:41:03 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460367082</guid>
      </item>
      <item>
         <title>First approach: the use of matrices</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460370087</link>
         <description><![CDATA[<div>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 (x<sub>i</sub>, y<sub>i</sub>), 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 <strong>matrices</strong> 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.&nbsp;<br><br>Matei, Petru, George</div>]]></description>
         <enclosure url="" />
         <pubDate>2023-01-29 15:46:02 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460370087</guid>
      </item>
      <item>
         <title>Updates from Cluj-Napoca</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460371490</link>
         <description><![CDATA[<div>Informatics approach #3:<br>We used the Monte Carlo algorithm to determine the approximate value of the number of rounds it takes the machine to always win.&nbsp;<br>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.<br><br>George, Petru, Matei<br><br></div>]]></description>
         <enclosure url="" />
         <pubDate>2023-01-29 15:48:22 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460371490</guid>
      </item>
      <item>
         <title>Updates from Cluj-Napoca</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460374996</link>
         <description><![CDATA[<div>Probabilistic approach:<br>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.<br>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.<br><br>George, Petru, Matei</div>]]></description>
         <enclosure url="" />
         <pubDate>2023-01-29 15:53:43 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460374996</guid>
      </item>
      <item>
         <title>Updates from Cluj-Napoca</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460378596</link>
         <description><![CDATA[<div>Mathematical approach:<br>We developed a recursion formula for smaller parameters.<br>starting from the case of two sticks, two cups we went on to develop recursions until the case with five sticks , five cups.<br>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.<br><br>George, Petru, Matei<br><br><br></div>]]></description>
         <enclosure url="" />
         <pubDate>2023-01-29 15:59:54 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460378596</guid>
      </item>
      <item>
         <title>Another approach: the least squares regression line</title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460383906</link>
         <description><![CDATA[<div>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.<br><br>Petru, Matei, George</div>]]></description>
         <enclosure url="" />
         <pubDate>2023-01-29 16:08:51 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2460383906</guid>
      </item>
      <item>
         <title>10/01/2023</title>
         <author>proalh</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2462062660</link>
         <description><![CDATA[<div>Presentation to the Val de Durance High School researcher.<br>Yves PAPEGAY - INRIA Sophia Antipolis</div>]]></description>
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         <pubDate>2023-01-30 20:28:30 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2462062660</guid>
      </item>
      <item>
         <title>Terminale group - Pertuis</title>
         <author>proalh</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2468505884</link>
         <description><![CDATA[<div>https://www.lyc-valdedurance.ac-aix-marseille.fr/spip/spip.php?article3136</div>]]></description>
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         <pubDate>2023-02-04 15:40:15 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2468505884</guid>
      </item>
      <item>
         <title>Presentation</title>
         <author>proalh</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2468506750</link>
         <description><![CDATA[]]></description>
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         <pubDate>2023-02-04 15:41:32 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2468506750</guid>
      </item>
      <item>
         <title>Elements to build the common presentation during the congress in Nice</title>
         <author>proalh</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2528279818</link>
         <description><![CDATA[]]></description>
         <enclosure url="https://padlet-uploads.storage.googleapis.com/833157256/53fce15adde64d856f000c5e20d12c7a/Front_page.pdf" />
         <pubDate>2023-03-23 05:11:15 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2528279818</guid>
      </item>
      <item>
         <title>MaSuD Logo</title>
         <author>proalh</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2528280763</link>
         <description><![CDATA[]]></description>
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         <pubDate>2023-03-23 05:11:49 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2528280763</guid>
      </item>
      <item>
         <title>Mej logo</title>
         <author>proalh</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2528281287</link>
         <description><![CDATA[]]></description>
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         <pubDate>2023-03-23 05:12:14 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2528281287</guid>
      </item>
      <item>
         <title>ERASMUS logo</title>
         <author>proalh</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2528281655</link>
         <description><![CDATA[]]></description>
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         <pubDate>2023-03-23 05:12:34 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2528281655</guid>
      </item>
      <item>
         <title></title>
         <author></author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2539599198</link>
         <description><![CDATA[<div>Hello! We made a few slides for the presentation. Feel free to complete it.</div>]]></description>
         <enclosure url="https://padlet-uploads.storage.googleapis.com/2010235815/b226976c716cd90bcb46ada7e83d43c4/THE_STICK_GAME.pptx" />
         <pubDate>2023-03-31 08:28:43 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2539599198</guid>
      </item>
      <item>
         <title>Presentations in Pertuis secondary schools</title>
         <author>hubertproal</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2637111049</link>
         <description><![CDATA[<div>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</div>]]></description>
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         <pubDate>2023-07-03 10:23:32 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2637111049</guid>
      </item>
      <item>
         <title>The video-conference (@Colegiul National Emil Racovita)</title>
         <author>arianavacaretu</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639406467</link>
         <description><![CDATA[]]></description>
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         <pubDate>2023-07-06 06:01:05 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639406467</guid>
      </item>
      <item>
         <title>The video-conference - the 10th graders group from CNER</title>
         <author>arianavacaretu</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639407824</link>
         <description><![CDATA[]]></description>
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         <pubDate>2023-07-06 06:02:56 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639407824</guid>
      </item>
      <item>
         <title>The video-conference - the 11th graders group from CNER</title>
         <author>arianavacaretu</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639409109</link>
         <description><![CDATA[]]></description>
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         <pubDate>2023-07-06 06:04:33 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639409109</guid>
      </item>
      <item>
         <title>Topic 1 @ the National Olympiad of Scientific Creativity (Cluj county) - 27 April 2023</title>
         <author>arianavacaretu</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639419443</link>
         <description><![CDATA[<div>Presentation of the research topic 1-The machine to play the sticks game &amp; 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.</div>]]></description>
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         <pubDate>2023-07-06 06:18:38 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639419443</guid>
      </item>
      <item>
         <title>Research poster (CNER - Cluj students)</title>
         <author>arianavacaretu</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639460013</link>
         <description><![CDATA[]]></description>
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         <pubDate>2023-07-06 07:15:20 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639460013</guid>
      </item>
      <item>
         <title>13/05/2023</title>
         <author>hubertproal</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639466757</link>
         <description><![CDATA[<div>MaSuD at the Faites de la science competition at the Faculté St Jérôme in Marseille&nbsp;<br>https://www.site.ac-aix-marseille.fr/lyc-valdedurance/spip/ERASMUS-MaSuD-au-concours-Faites-de-la-science.html<br><br></div>]]></description>
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         <pubDate>2023-07-06 07:25:15 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639466757</guid>
      </item>
      <item>
         <title>A poster from a group in Pertuis</title>
         <author>hubertproal</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639468164</link>
         <description><![CDATA[]]></description>
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         <pubDate>2023-07-06 07:26:53 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639468164</guid>
      </item>
      <item>
         <title>06/04/2023</title>
         <author>hubertproal</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639470198</link>
         <description><![CDATA[<div>Slide presentation at the MATh.en.JEANS Congress in Nice</div>]]></description>
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         <pubDate>2023-07-06 07:29:37 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639470198</guid>
      </item>
      <item>
         <title>A poster from a group in Pertuis</title>
         <author>hubertproal</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639472770</link>
         <description><![CDATA[]]></description>
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         <pubDate>2023-07-06 07:33:37 UTC</pubDate>
         <guid>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2639472770</guid>
      </item>
      <item>
         <title>Topic 1 @ the National Olympiad of Scientific Creativity (national level) - Suceava University 5-9 July 2023</title>
         <author>arianavacaretu</author>
         <link>https://padlet.com/proalh/isd27i55rpj2tlf8/wish/2642510082</link>
         <description><![CDATA[<div>Petra Hedeșiu &amp; Matei Bojan presented the research topic &amp; their findings at the national level of the National Olympiad of Scientific Creativity. They were rewarded with the Suceava University honorable mention prize.</div>]]></description>
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         <pubDate>2023-07-11 06:41:27 UTC</pubDate>
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         <title>The research article</title>
         <author>arianavacaretu</author>
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         <pubDate>2023-07-20 20:28:09 UTC</pubDate>
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