Problem 3. Consider the 127-hat game. (a) How big is the H-matrix for this game? What is its 30th column? (b) Provide two losing congurations.

Consider the 255-hat game.

(a) How big is the H-matrix for this game? What is its 31st column? What is the 62nd column?

(b) Provide two losing configurations. Explain.

(c) How many losing configurations are there? Explain.

(d) Suppose there are 7 players with red hatsthose whose numbers are multiples of 36, and the rest have blue hats. How would each of the 255 players vote?

(e) Is the configuration of (d) winning?

The below images are an example from last year, just with the variables changed, still confused though please help!

• Attachment 1
• Attachment 2

Problem 3. Consider the 127-hat game.(a) How big is the H-matrix for this game? What is its 30th column?(b) Provide two losing configurations. Explain. (c) How many losing configurations are there?I Explain. 2 [11) Suppose thorn are 7 players with red hats—those whose numbers are multiples of 18,and the rest have blue hats. How would each of the 127 plays-rs vote? (9.} Is the configuration of {(1) Winning? Solution. (a) H is a 7 x 127 matrix. The 30th column would be the binary representation 0 O 1of 30 which is 1 . l 1 O