MathDB

1

Part of 2016 Tuymaada Olympiad

Problems(2)

Easy sequence

Source: tuymaada 2016, P1 Seniors

7/22/2016
The sequence (an)(a_n) is defined by a1=0a_1=0, an+1=a1+a2+…+ann+1. a_{n+1}={a_1+a_2+\ldots+a_n\over n}+1. Prove that a2016>12+a1000a_{2016}>{1\over 2}+a_{1000}.
algebraSequenceeasyOlympiadalgebra solved
tuymaada 2016/junior P1

Source:

7/22/2016
Tanya and Serezha have a heap of 20162016 candies. They make moves in turn, Tanya moves first. At each move a player can eat either one candy or (if the number of candies is even at the moment) exactly half of all candies. The player that cannot move loses. Which of the players has a winning strategy?
combinatoricsCombinatorial games