There is a game in which two people can play. One person writes down a positive integer. The second person looks at it and decides whetherto go first or second. The players then take turns subtractig powers of 2 (i.e. 1,2,4,8,16,... no fractional or negative powers allowd) from the original number. negatives are not allowed and the player who gets to 0 wins. Assuming both players are playing to win and you did not write down the numebr:
1. What should you do if 3 is the chosen number?
2. What should yo do if 5 is the chosen number?
3. What are all the starting numbers from 1-20 in which you would want to go first?
4. Develop a plan of whether to go first or second for all starting numbers from 1-100.
5. If you played the game by subtracting powers of 3, what would your strategy be?
I need to prepare a document to explaining the solution to all of the above problems. Please help....