The game of Nim. This is a well-known game with a number of variants. We will consider the following variants, which has an interesting winning strategy. Two players alternately take marbles from a pile. In each move, a player chooses how many marbles to take. The player must take at least one but at most half of the marbles. Then the other player takes a turn. The player who takes the last marble loses.

Write a program and create a Flow Chart in which computer plays against a human opponent. Generate a random integer between 10 and 100 to denote the initial size of the pile. Generate a random integer between 0 and 1 to decide whether the computer or the human takes the first turn. Generate a random integer between 0 and 1 to decide whether the computer plays smart or stupid. In stupid model, the computer simply takes a random legal value (between 1 and n/2) from the pile whenever it has a turn. In smart model the computer takes off enough marbles to make the size of the pile a power of 2 minus 1 - that is, 3, 7, 15, 31, or 63. This is always a legal move, except if the size of the pile is currently one less than a power of 2. In that case, the computer makes a random legal move.

Create a flow chart.

Note that the computer cannot be beaten in smart mode when it has the first move, unless the pile size happens to be 15, 31, or 63. Of course, a human player who has the first turn and knows the winning strategy can win against the computer.