IMO Shortlist 2007

... present other two constructions for j ≤ 2007, without proof: g j (n) =      1, n < 2007, j, n = 2007, n, n > 2007; h j (n) = max  1,  jn 2007  . Also the example for j = 2008 can ... f (2007) ≤ 2008. Now we present a family of examples showing that all values from 1 to 2008 can be realized. Let f j (n) = max{1, n + j 2007} for j = 1, 2, . . . , 2007; f 2008 (n) =  n,...

Ngày tải lên: 02/06/2014, 16:36

Ngày tải lên: 02/06/2014, 16:33

... by 2 t k , which completes the argument. 47 th International Mathematical Olympiad Slovenia 2006 Shortlisted Problems with Solutions 29 C6. A holey triangle is an upward equilateral triangle of

Ngày tải lên: 02/06/2014, 16:35

... extreme shortage of easy and appr opriate submissions forced the Problem Selection Committee to shortlist a simplified variant. The same one-dimensional Claim is used in both versions. Original ... element of S b is b + 1, a contradiction. 49 th International Mathematical Olympiad Spain 2008 Shortlisted Problems with Solutions Geometry G1. In an acute-angled triangle ABC, point H is the

Ngày tải lên: 02/06/2014, 16:37

... 1, j is a TL-block, thus the 51 st International Mathematical Olympiad Astana, Kazakhstan 2010 Shortlisted Problems with Solutions 29 i 1 th row is a n L-row. Now, choosing the ith row to be

Ngày tải lên: 02/06/2014, 16:42