# Slider Puzzle: Lesson 7

### From OLPC

## Slider Puzzle Lesson 7: The n-puzzle (Mathematical Patterns and Sequences)

The ** n-puzzle** is general name for a slider puzzle that

**consists of a grid of numbered squares with one square missing, and the numbers out of sequence**. The 9-puzzle is a 3×3 numbered grid, the 16 puzzle is a 4×4 numbered grid. The goal of the n-puzzle is put the scrambled numbers back in sequence.

**The n-puzzle is a classical problem for modeling repeatable steps (or “algorithms”) involving mathematical patterns (or “heuristics.”)** For example, you can begin by counting the number of misplaced tiles as you formulate a strategy for solving the puzzle. The n-puzzle also helps students to understand that some tile arrangements are unsolvable.

**Skills:**

- Recognize patterns.
- Practice classification and grouping.
- Practice sequencing.
- Put numbers in order.

**Activity:**

1) **Start the Slider Puzzle** activity and **choose the category labeled “Sequencing.”** Sequencing is when you put things into a logical order.

2) **When the first image comes up, think how this image is set up differently from the one on the Slider Puzzle.** The Slider Puzzle creates a large image, where all the squares are pieces of the larger image, while the Sequencing image contains a number on each tile.

3) **Try to solve the 9-tile puzzle first. Try to put the numbers in order from smallest to largest.** Model for other students how to slide the keys and place them in order.

4) **Once you are able to solve the 9-puzzle, share your strategies with the class.** How is this different from the Slider Puzzles where you are assembling a picture?

5) **Now try to solve the 16-puzzle. How is this harder or easier?**

6) After completing the 16-puzzle, **walk around and help those who are having trouble.**