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Category Archives: Homework
Combinatorial Game Theory Quiz 3
The quiz lasts 75 minutes and covers everything from lessons 112. For each of the following Nim games, find one good move for the first player, if any. (10 points) [ Note : exactly one of the games is a … Continue reading
Combinatorial Game Theory Quiz 2
This quiz lasts 70 minutes and covers materials from lessons 19. Use the simplicity rule to compute the values of the following games. (10 points) {1/2  } {1/4  } {1/8  3/8} {0  7/8} {1/8  9/16} … Continue reading
Posted in Homework
Tagged combinatorial game theory, computer science, game numbers, intermediate, partial games, up game
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Combinatorial Game Theory Quiz 1
This quiz lasts 70 minutes and covers materials from lessons 14. For AC, determine whether the following Nim games are first or secondplayer wins. There is no need to find the winning move. (10 points) (10, 15, 17, 19) (7, … Continue reading
Posted in Homework
Tagged basic, combinatorial game theory, computer science, impartial games, nim, nim values
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Number Theory Homework (2 Weeks)
Homework problems for 5 Nov 2011: Let a1, a2, … be a series recursively defined as follows: a1 = 20, a2 = 11, and for n ≥ 1, an+2 is the remainder when an+1 + an is divided by 100. … Continue reading
Homework (29 Oct 2011)
The homework for last week was a little harder than the prior one: Let n be a positive integer, . Prove that the sum of the divisors of n is a multiple of 24. Let N = 210 × 39 … Continue reading
Homework (22 Oct 2011)
Here’re the problems: A square integer N ends in 4 identical digits d in its decimal representation, where . Find all possible values of d. For each admissable value of d, find a possible N. N is a perfect square whose secondtolast … Continue reading