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Math 111

Assignment 3

1. [5 marks]

(a) For the 63-hat game, what is the 45th column of the H-matrix?

(b) Suppose that in the 63-hat game there are 11 players with red hats––those whose numbers are between 35 and 45 inclusive. What does each of the 63 players write on her slip of paper?

2. [6 marks] This problem concerns the code based on the 31-hat game. Here the message should be decomposed into blocks of length 31–5 = 26. Suppose that one of the 26-blocks in the starting message has eight 0’s followed by ten 1’s, followed by eight 0’s. That is, it is

(a) Find its associated L-node, which is the code word that will be transmitted.

(b) Suppose that in the transmission, there is an error in the 20th character. Give a detailed account of the calculations made by the decoder to recover the original message.

3. [5 marks] Now consider the 7-hat game and suppose that players numbered 1 and 2 have written RED and player 3 has written BLUE on their slips of paper. What can you say about the colours of all the hats?