MathDB

6

Part of 2017 Thailand TSTST

Problems(2)

Game Theory

Source: 2016 Thailand October Camp 1.6

2/26/2022
AA and BB plays a game, with AA choosing a positive integer n∈{1,2,…,1001}=Sn \in \{1, 2, \dots, 1001\} = S. BB must guess the value of nn by choosing several subsets of SS, then AA will tell BB how many subsets nn is in. BB will do this three times selecting k1,k2k_1, k_2 then k3k_3 subsets of SS each.
What is the least value of k1+k2+k3k_1 + k_2 + k_3 such that BB has a strategy to correctly guess the value of nn no matter what AA chooses?
Game Theorycombinatorics
f(xy)+f(yz)+f(zx)=f(xy+yz+zx), x+y+z=0

Source: 2022 Thailand October Camp 2.6

2/26/2022
Find all polynomials ff with real coefficients such that for all reals x,y,zx, y, z such that x+y+z=0x+y+z =0, the following relation holds: f(xy)+f(yz)+f(zx)=f(xy+yz+zx).f(xy) + f(yz) + f(zx) = f(xy + yz + zx).
polynomialalgebra