MathDB

Game Theory

Source: 2016 Thailand October Camp 1.6

February 26, 2022

Game Theorycombinatorics

Problem Statement

A

and

B

plays a game, with

A

choosing a positive integer

n \in \{1, 2, \dots, 1001\} = S

.

B

must guess the value of

n

by choosing several subsets of

S

, then

A

will tell

B

how many subsets

n

is in.

B

will do this three times selecting

k_1, k_2

then

k_3

subsets of

S

each.
What is the least value of

k_1 + k_2 + k_3

such that

B

has a strategy to correctly guess the value of

n

no matter what

A

chooses?

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