1. Interpret integers and other numbers written in base b for some integer b that is not 0, 1, or -1. Note that b can be negative.
2. Given an integer in decimal notation, and a base b, find the base b representation of the integer using both repeated subtraction and repeated division. Justify the use of repeated division.
3. Given a non-integer x and a base b, find the base b representation of x.
4. Construct the multiplication and addition tables for digits in a given base b, and use these tables to perform arithmetic in that base.
5. Given a base b repeating expression, find a pair of integers whose
quotient is the given expression.
1. Find the binary configuration of a position in Bouton's Nim and use nim addition to determine whether the position is safe or unsafe (ie, Grundy value 0 or not). Find all move to safe positions from a given unsafe position.Study Guide for Test 2
2. Analyze simple games, like N(20; 1,3,6) to determine the Grunday values of all the positions in the game.
3. Analyze "games" which are not really games in the sense that strategies cannot effect the outcome. These games often have a fixed number of moves independent of what stategies are employed. Some of these games have a variable number of moves, but must be won by the second player because the number of counters alternates between even and odd. An example of such a game is N(20;1,3,5).
4. Understand the use of symmetry in certain games, like Kram.
5. Carry out the "Grundy analysis on two-pile games, like Wythoff's game.
6. Use Nim addition of Grundy values to play a composition of several games.