Consider the problem of solving two 8-puzzles.

a. Give a complete problem formulation.
b. How large is the reachable state space? Give an exact numerical expression.
c. Suppose we make the problem adversarial as follows: the two players take turns moving; a coin is flipped to determine the puzzle on which to make a move in that turn; and the winner is the first to solve one puzzle. Which algorithm can be used to choose a move in this setting?
d. Give an informal proof that someone will eventually win if both play perfectly.

Given a link with a maximum transmission rate of 32.8 mbps. only two computers, x and y, wish to transmit starting at time t = 0 seconds. computer x sends filex (4 mib) and computer y sends filey (244 kib), both starting at time t = 0. statistical multiplexing is used, with details as follows packet payload size = 1000 bytes packet header size = 24 bytes (overhead) ignore processing and queueing delays assume partial packets (packets consisting of less than 1000 bytes of data) are padded so that they are the same size as full packets. assume continuous alternating-packet transmission. computer x gets the transmission medium first. at what time (t = ? ) would filey finish transmitting? give answer in milliseconds, without units, and round to one decimal places (e.g. for an answer of 0.013777 seconds you would enter "13.8" without the quotes)