Bariz - Problem

Hi everyone, In a week there will be the 4th edition of Oliforum Contest: it's an individual and telematic contest, with some training problems at national/imo level. There will be no prize, but it can be useful to some forumers around here. All the details in the following list: 1- The contest is made by a unique round, starting in the morning of 1 october, and ending at 23:59 of 6 october (Rome meridian +1GTM): that is, 6 days. 2- Every problem will have some points, from 0 to 7: in particular, 6 for all correct solutions and 7 only for clear and original ones. 3- Everyone can send his solutions: there are no age contraints. 4- Non-olympic arguments cannot be used, otherwise the solution is not going to be valid. 5- It's enough to send the solution by mail, that you can find below. Enrollment is not necessary. 6- Time of incoming solutions will be considered only for ex-aequo positions. 7- How to send solutions. - You need to send solutions to the following mail: $\text{ leonetti.paolo (AT) gmail.com }$. - Solutions need to be attached in a unique attached .pdf file with a reasonable size. - The .pdf file must be written with $\LaTeX$ or in a way that can be easily understood. - You have to rename the .pdf file with the nickname that you have here on MathLinks. - Do not write anything else in the mail, unless strictly necessary. - Try to be clear everytime. Previous editions: { Ed. 2008, round 1, round 2, round 3 } , { Ed. 2009, round 1, round 2 }, { Ed. 2012 round 1 }. I'll put below the list of problems on the morning of 1 october 2013: later, the list with all people who sent correctly their solutions will be added. Any comment and/or suggestion will be welcome. Thanks for the attention Paolo Leonetti Italian version