Puzzles and Games

This collection includes a number of logic puzzle applets and presents approaches for modeling and solving them as optimization problems.

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.

Abbott’s Window Puzzle

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.

NY Times Circuitboard Puzzle

You want to connect the points on the circuit board so that every point is connected to either one or three (never two) other points, and so that no areas are enclosed. When you're done, all the points must be interconnected.

Rogo Puzzle

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.

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 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.