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We study variants of Mastermind, a popular board game in which the objective is sequence reconstruction. In this two-player game, the so-called codemaker constructs a hidden sequence H = ( h 1 , h 2 , … , h n ) of colors selected from an alphabet A = { 1 , 2 , … , k } (i.e., h i ∈ A for all i ∈ { 1 , 2 , … , n } ). The game then proceeds in turns, each of which...
We consider the following two-player game, parametrised by positive integers n and k . The game is played between Painter and Builder, alternately taking turns, with Painter moving first. The game starts with the empty graph on n vertices. In each round Painter colours a vertex of her choice by one of the k colours and Builder adds an edge between two previously unconnected vertices. Both players...
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