Skip to main content\( \newcommand{\identity}{\mathrm{id}}
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Chapter 23 The Game of Nimble
Exercises Practice Problems
1.
Alice and Bob play the following games of Nimble. Alice goes first. Decide who has a winning strategy. Mark each game as "Alice Win" or "Bob Win" next to each board, as appropriate.
Solution.
Alice win
Bob win
Alice win
Alice win
Bob win
Alice win
2.
Create the complete game trees for positions (a) and (b) above. Label the leaves (terminal positions) as \(\cP\) and then work your way up the tree, marking each position with an \(\cN\) or a \(\cP\text{.}\) Remember to follow the two rules:
Solution.
3.
Create the complete game tree for position (c) above, as you did in problem 2. Mark each position with an \(\cN\) or a \(\cP\text{.}\) Once you are done, compare your answer to this problem with the trees in problem 2. Make any useful observations that you can. Solution.
