The Hats Game. the Power of Constructors

We analyze the following general version of deterministic Hats game. Several sages wearing colored hats occupy vertices a graph. Each sage can have hat one k colors. tries to guess color his own merely on basis observing neighbors without exchanging any information. A predetermined guessing strategy is winning if it guarantees at least correct individual for every assignment present an example planar graph which win = 14. also give easy proof theorem about game “windmill” graphs.