نتایج جستجو برای: olympiad
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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...
The Australian Computational and Linguistics Olympiad (OzCLO) started in 2008 in only two locations and has since grown to a nationwide competition with almost 1500 high school students participating in 2013. An Australian team has participated in the International Linguistics Olympiad (ILO) every year since 2009. This paper describes how the competition is run (with a regional First Round and ...
A detailed overview of the problems, solutions and experience of the first international student’s Olympiad in cryptography, NSUCRYPTO’2014, is given. We start with rules of participation and description of rounds. All 15 problems of the Olympiad and their solutions are considered in detail. There are discussed solutions of the mathematical problems related to cipher constructing such as studyi...
Best Student Paper Award in the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2006. Distinction in Teaching Honor to be awarded by CS Department, Stanford University. Best Summer Project Award, IBM India Research Lab, 2000. Young Engineering Fellowship offered by IISc, Bangalore, India – Selection in 2000. Summer Research Fellowship offered by Jawaharlal Nehru Center for ...
4. Let P be a point inside triangle ABC. The lines AP, BP, and CP intersect the circumcircle of triangle ABC again at the points K , L , and M , respectively. The tangent to at C intersects the line AB at S. Suppose that SC = SP. Prove that MK = ML. 5. In each of six boxes B1, B2, B3, B4, B5, B6 there is initially one coin. There are two types of operation allowed: Type 1: Choose a nonempty box...
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