# Puzzles

This collection includes a number of logic puzzle applets and presents approaches for modeling and solving them as optimization problems. For the best results, we recommend using Firefox for these interactive case studies.

• Rubik's Cube
Given an $n \times n \times n$ Rubik's cube, this study describes a model whose objective is to minimize the number of turns needed to solve the cube.
• The Abbott's Window
Given a $n \times n$ grid of panes, the objective of the Abbott's Window puzzle is to maximize the number of lighted panes subject to the constraint that the number of lighted panes in every row, column, and diagonal is even.
• Rogo
Given a $n \times m$ grid with numbered cells and forbidden cells, the objective of the Rogo puzzle is to find a loop of fixed length through the grid such that the sum of the numbers in the cells on the loop is maximized.
• Sudoku
The objective of sudoku is to fill a 9 x 9 grid so that each column, each row, and each of the nine 3 x 3 boxes contains all of the digits from 1 to 9 exactly once.
• 15 Puzzle
The objective of the 15 Puzzle is to place the 15 numbered tiles in order by making sliding moves that use the empty space.