ĐỀ THI TOÁN APMO (CHÂU Á THÁI BÌNH DƯƠNG) ĐỀ 33 pot
ĐỀ THI TOÁN APMO (CHÂU Á THÁI BÌNH DƯƠNG)_ĐỀ 33 pot
... from its two neighbours A i−1 and A i+1 . (Here A n+1 means A 1 and A n means A 0 .) How should this redistribution be performed so that the total number of objects transferred is minimum?
Ngày tải lên: 05/08/2014, 10:21
ĐỀ THI TOÁN APMO (CHÂU Á THÁI BÌNH DƯƠNG)_ĐỀ 12 pot
... < 180 ◦ − ( ∠B + ∠C 2 ) = 90 + ∠A 2 < 120 ◦ . In this way, a special case of the problem can be easily proved. 2 again by induction hypothesis. Combining (†), (‡) and f(2 k − 1) = f(2(2 k−1 − ... we obtain a k = 2a k−1 + 2 k−1 − 1 for all k ≥ 3. Note that this recursive formula for a k also holds for k ≥ 0, 1 and 2. Unwinding this recursive formula, we finally get a k = 2a k−1 + 2 k−1 −...
Ngày tải lên: 05/08/2014, 10:22
