# Slider Puzzle: Lesson 7

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## 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.

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