An ‘in shuffle’ is a perfect riffle shuffle on a standard deck of 52 playing cards - that just means a shuffle by splitting the deck in half, then interleaving cards, starting with the top half. Can you write a quick program to solve the following? What is the position of the first card after the 7th shuffle?
How many times must you perform the shuffle so that the top card becomes the bottom card?
When do the first and last cards in the deck touch?
Finally, about how much time did you spend on this problem?

Think about some of the most memorable and forgettable games ever created. they can be games that were discussed in this unit or otherwise. what are some of the consistent factors that made certain games memorable to you? what were some of the consistent factors that made certain games forgettable to you? why? explain.

Write a program called assignment3 (saved in a file assignment3.java) that computes the greatest common divisor of two given integers. one of the oldest numerical algorithms was described by the greek mathematician, euclid, in 300 b. c. it is a simple but very e↵ective algorithm that computes the greatest common divisor of two given integers. for instance, given integers 24 and 18, the greatest common divisor is 6, because 6 is the largest integer that divides evenly into both 24 and 18. we will denote the greatest common divisor of x and y as gcd(x, y). the algorithm is based on the clever idea that the gcd(x, y) = gcd(x ! y, y) if x > = y and gcd(x, y) = gcd(x, y ! x) if x < y. the algorithm consists of a series of steps (loop iterations) where the “larger” integer is replaced by the di↵erence of the larger and smaller integer. this continues until the two values are equal. that is then the gcd.

Consider a byte-addressable computer with 16mb of main memory, a cache capable of storing a total of 64kb of data and block size of 32 bytes. (a) how many bits in the memory address? (b) how many blocks are in the cache? (c) specify the format of the memory address, including names and sizes, when the cache is: 1. direct-mapped 2. 4-way set associative 3. fully associative