MathDB

2

Part of 2015 CHMMC (Fall)

Problems(2)

2015 Fall Team #2

Source:

3/26/2022
You have 44 game pieces, and you play a game against an intelligent opponent who has 66. The rules go as follows: you distribute your pieces among two points a and b, and your opponent simultaneously does as well (so neither player sees what the other is doing). You win the round if you have more pieces than them on either aa orb b, and you lose the round if you only draw or have fewer pieces on both. You play the optimal strategy, assuming your opponent will play with the strategy that beats your strategy most frequently. What proportion of the time will you win?
combinatorics
2015 CHMMC Tiebreaker 2 - a_{n+1} =1/n a_n + a_{n-1}

Source:

3/1/2024
Let a1=1a_1 = 1, a2=1a_2 = 1, and for n≥2n \ge 2, let an+1=1nan+an−1.a_{n+1} =\frac{1}{n} a_n + a_{n-1}. What is a12a_{12}?
algebrarecurrence relationCHMMC