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Some maths problems....

Hey guys!! if you could help me with any of these questions, that would be great! thanks:

1.consider the following three 2 player games. For each game determine whether there is a winning strategy, if there is a winning strategy, describe it, try to find ways to generalise the game and the strategy.

"31" Players take turn to choose a number between 1 and 6 (inclusive), keeping a running total. The player who makes the running total equal to 31 is the winner. (this ones abit like that 21 dares game)

"Piles" There are two piles of matches. Players take turns taking away matches: either any number of matches from a single pile, or the same number of matches from both piles. The winner is the player who takes the last match

"cartesian dash" this game is played on a rectangular grid. The first player puts a cross in the bottom left hand square. Players then take turns to put a cross in a square next to the cross just placed - either immediately to the right or directly above or diagonally up and right. The winner is the person who puts the cross in the top right hand corner of the grid.

2. "drug dosage" to control a certain illness, a patient needs to take medicine. The effect of the medicine depends on its concentration in the patient's blood. This concentration increases when the patient take a dose of the medicine, and then starts to decrease, Above a certain concentration the medicine starts to have unpleasant side effects; if the concentration gets too low then the medicine stops being effective and the illness' symptoms come back.
How should the patient take the medicine.

3. "Growth of Bacteria" We have a infestation of bacteria in a greenhouse. On a certain day, there are 10^5 individual bacteria. Each day, the population increases by 32% because some of them divide. However, each day we clean the greenhouse, we remove 3 x 10^4 of them.
i. Determine the number of bacteria there will be on any given day
ii. How does your answer chance if we are able to remove 5 x 10^4 bacteria each day?
iii. Generalise this.

Thanks for any help given....Realistic assumptions can be made.