Category Archives: Homework

Combinatorial Game Theory Quiz 3

Posted on September 9, 2012 by limsup

The quiz lasts 75 minutes and covers everything from lessons 1-12. 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 →

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Combinatorial Game Theory Quiz 2

Posted on August 21, 2012 by limsup

This quiz lasts 70 minutes and covers materials from lessons 1-9. 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 →

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Combinatorial Game Theory Quiz 1

Posted on August 8, 2012 by limsup

This quiz lasts 70 minutes and covers materials from lessons 1-4. For A-C, determine whether the following Nim games are first or second-player wins. There is no need to find the winning move. (10 points) (10, 15, 17, 19) (7, … Continue reading →

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Number Theory Homework (2 Weeks)

Posted on November 14, 2011 by limsup

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 →

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Homework (29 Oct 2011)

Posted on November 4, 2011 by limsup

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 →

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Homework (22 Oct 2011)

Posted on October 27, 2011 by limsup

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 second-to-last … Continue reading →

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