#1. For SUBTRACTION({2,3,5,8}), fill out a table for single pile sizes n, with 0 ≤ n ≤ 16, in each case
indicating the outcome class (P or N) for each n and also the smallest good move (the least number of
markers to remove) for a position involving a single pile of size n. No work required.
#2. For SUBTRACTION({3,4,8}), fill out a table for single pile sizes n, with 0 ≤ n ≤ 16, in each case
indicating the outcome class for each n and list each good move. Indicate a repeating pattern for the
locations of the P-positions, using the “two box” method for showing the pattern. No work required.
#3. For analyzing CUTTHROAT STARS positions involving any number of stars (each with 1 or more
edges), it turns out to be very convenient to compute each of the following amounts:
d = the number of stars having an odd number of edges, and
e = the number of stars having an even number of edges.
(i) Make a conjecture as to which CUTTHROAT STARS positions are P-positions and which are N–
positions. No work required.
Let CP denote the set of positions that you conjecture are P-positions, and let CN denote the set of
positions that you conjecture are N-positions. HINT: it turns out that all positions with d,e both odd have
the same outcome class (N or P), and that all positions with d,e both even have the same outcome class
(N or P), and that all positions with d odd and e even have the same outcome class (N or P), and that all
positions with e odd and d even have the same outcome class (N or P).
#4. For QUEEN, fill out a 16 by 16 grid, indicating for each (x,y) whether it is a P-position or
N-position, for 0 ≤ x,y ≤ 15. No work required. If desired, you may print out the following chart. In
your grid, you need only mark with P’s the locations of the P-positions, leaving blank the locations for
the N-positions.
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