th International Mathematical Olympiad
نویسندگان
چکیده
2. A configuration of 4027 points in the plane is called Colombian if it consists of 2013 red points and 2014 blue points, and no three of the points of the configuration are collinear. By drawing some lines, the plane is divided into several regions. An arrangement of lines is good for a Colombian configuration if the following two conditions are satisfied: • no line passes through any point of the configuration; • no region contains points of both colours.
منابع مشابه
Mathematical methods in solutions of the problems from the Third International Students' Olympiad in Cryptography
The mathematical problems and their solutions of the Third International Students’ Olympiad in Cryptography NSUCRYPTO’2016 are presented. We consider mathematical problems related to the construction of algebraic immune vectorial Boolean functions and big Fermat numbers, problems about secrete sharing schemes and pseudorandom binary sequences, biometric cryptosystems and the blockchain technolo...
متن کاملA Proposal for an IOI Syllabus
The International Olympiad in Informatics (IOI) is the premier competition in computing science for secondary education. The competition problems are algorithmic in nature, but the IOI Regulations do not clearly define the scope of the competition. The international olympiads in physics, chemistry, and biology do have an official syllabus, whereas the International Mathematical Olympiad has mad...
متن کاملInformatics olympiads: Approaching mathematics through code
Many readers are familiar with the International Mathematical Olympiad (IMO), a pinnacle in the yearly calendar of mathematics competitions. Here we introduce its cousin in computer science, the International Olympiad in Informatics (IOI). The International Olympiad in Informatics is one of the newer Science Olympiads, beginning in 1989 in Bulgaria under the leadership of Petar Kenderov. In its...
متن کاملSolutions to the 73rd William Lowell Putnam Mathematical Competition Saturday, December 1, 2012
A–1 Without loss of generality, assume d1 ≤ d2 ≤ ·· · ≤ d12. If d2 i+2 < d 2 i + d 2 i+1 for some i ≤ 10, then di,di+1,di+2 are the side lengths of an acute triangle, since in this case d2 i < d 2 i+1+d 2 i+2 and d 2 i+1 < d 2 i +d 2 i+2 as well. Thus we may assume d2 i+2 ≥ d2 i + d2 i+1 for all i. But then by induction, d2 i ≥ Fid 1 for all i, where Fi is the i-th Fibonacci number (with F1 = F...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015