1. The game of Boggle consists of a grid of letters and a word list. The object is to ?nd words in the grid subject to the constraint that two adjacent letters must be adjacent in the grid and each item in the grid can be used, at most, once per word. Write a program to play Boggle.

2. Write a program to play MAXIT. The board is represented as an N-by-N grid of numbers randomly placed at the start of the game. One position is designated as the initial current position. Two players alternate turns. At each turn, a player must select a grid element in the current row or column. The value of the selected position is added to the player's score, and that position becomes the current position and cannot be selected again. Players alternate until all grid elements in the current row and column are already selected, at which point the game ends and the player with the higher score wins.

3. Othello played on a six-by-six board is a forced win for black. Prove this by writing a program. What is the ?nal score if play on both sides is optimal?