IMO Shortlist 2008

... least 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 ... 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

Ngày tải lên: 02/06/2014, 16:37

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

... former case we have f 2008 (m) = m, while in the latter one f 2008  f 2008 (n)  = f 2008 (n) = n, providing f 2008 (m) + f 2008  f 2008 (n)  − 1 ≤ (m + n + 1) −1 = f 2008 (m + n). 11 Comment. ... + 1 and hence n + 1 = f 2008 (n + 1) = f 2008  f 2008 (n)  . So, if 2007   m + n, then f 2008 (m + n) = m + n + 1 = (m + 1) + (n + 1) − 1 ≥ f 2008 (m) + f 2008  f...

Ngày tải lên: 02/06/2014, 16:36

... 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