Hello Everyone brave enough to tackle this:

if I have:

Ncompetitors- (
N-1competitors for1competitor to compete against)Xsudoku puzzles1competition consists of10sudoku puzzlesXsudoku puzzles from which a competition of10sudoku puzzles arerandomlychosen- to choose the
1stsudoku puzzle (of 10) there areXchoices- to choose the
2ndsudoku puzzle (of 10) there areX-1choices- to choose the
3rdsudoku puzzle (of 10) there areX-2choices- to choose the
4thsudoku puzzle (of 10) there areX-3choices- to choose the
5thsudoku puzzle (of 10) there areX-4choices- etc...
- to choose the
10thsudoku puzzle (of 10) there areX-9choices- There are
P'one vs. one' competitions, in which the two competitors face the same10sudoku puzzles.- There are
Q'one vs. group' competitions, a group consists ofMcompetitors, in which all the competitors face the same10sudoku puzzles.- There are
R'group vs. group' competitions, competing groups can be of different sizes, in which all theMcompetitors from the 2 different groups face the same10sudoku puzzles.- there are, at any one moment, a varied number of 'one vs. one' competitions and a maximum of
N/2'one vs. one' competitions each involving the completion of10sudoku puzzles to be chosen at random from the bank ofXsudoku puzzles- there are, at any one moment, a varied number of 'one vs. group' competitions each involving the completion of
10sudoku puzzles to be chosen at random from the bank ofXsudoku puzzles- there are, at any one moment, a varied number of 'group vs. group' competitions each involving the completion of
10sudoku puzzles to be chosen at random from the bank ofXsudoku puzzles- at any one moment, there are a number of 'one vs. one', 'one vs. group' and 'group vs. group' competitions occuring
- each player never faces the same sudoku puzzle twice irrespective of competing as an individual or in a group, he or she always completes a new sudoku puzzle but that same sudoku puzzle can be played by any and all players as long as they too have not played this sudoku puzzle before.
- the same 10 sudoku puzzles can be offered to competitors in competitions P, Q and R occuring at the same time as long as all or any one of the competitors involved had not faced any one of these 10 sudoku puzzles previously.
Question 1: What equation/formula captures the relationship between variablesN,X,M,P,QandR. Assumptions can be made for the value forM,P,QandRfor a certain scenario?

Question 2:Which scenario results in the quickest depletion of the bank ofXsudoku puzzles?