• Initially, there are 20 numbers:10 numbers 1 and 10 numbers 2.
• On each step one of the players select two numbers; and if they were the same, replace them by 2; otherwise, replace them by 1.
• Alice make the first move and they do moves one after another. Alice wins if the last number is 1 and Bob wins if the last number is 2. Who is the winner? Note that this game is not a combinatorial game
2. In the subtraction game where players may subtract 1, 2 or 5 chips on their turn, identify the N and P positions.
3. Is the Nim position (1,3,5) an N-position (explain your answer)?
4. Consider the Misere subtraction game where players may subtract 1, 5 or 6 chips on their turn, identify the N and P positions.
By purchasing this solution you'll be able to access the following files: