Table Tennis
All standard rules apply (see http://www.ittf.com/ITTF_Hand_Book/Hand_Book_html.html)
Every match till the semifinals will be best of three 11-point games
Semifinals and finals will be best of five 11-point games
You can bring your own team or we can draw it by lots at the venue

Carrom
All standard rules apply (see http://www.carrom.org/)
Four boards will be played for each match. The player/team with maximum points will win
In case of a tie, the player/team which won more boards is the winner
If the tie is still unresolved, a tie breaker will be played

Chess
All standard rules apply (see http://www.usachess.org/)

Sudoku

You will be provided a 9x9 grid with few cells containing single digits. The only rule is you need to complete the grid such that every row, every column and every 3x3 box contains a unique occurrence of the digits 1 to 9. (see http://www.sudoku.com/rule.htm)