Skyscrapers
How it works
Imagine that you have a set of towers — three that are 1 unit tall, three that are 2 units tall, and three that are 3 units tall. Your goal is to arrange these 9 towers in a 3 x 3 grid so that there is one (and only one) tower of each type in each row and in each column. To make things more interesting, there may be some additional requirements as well: For example, it might be required that the tower in a specific location must be a certain height, or that the tower in a specific location must be taller or shorter than one of its neighbors.
In this activity, students explore a variety of logic puzzles based on these rules. Some of these puzzles are possible, and some are impossible! Students explore puzzles on both 3 x 3 grids and 4 x 4 grids – on a 4 x 4 grid, there are four 1-unit towers, four 2-unit towers, four 3-unit towers, and four 4-unit towers – and the puzzles become increasingly challenging.
Why we like this activity
- It's fun! Students enjoy placing the towers and trying to solve the puzzles.
- It helps students to develop logical reasoning.
It requires students to engage in mathematical habits of mind:
Using logic to figure out where certain towers can and can't go.
Using logic to determine when a puzzle is impossible.
Finding and using strategies to solve puzzles efficiently (without guessing).
- It has a low floor and a high ceiling: Students can get started exploring using basic logic and trial and error, but as the puzzles get more challenging, it's useful to develop more effective strategies.
This activity was adapted from puzzles from the Julia Robinson Mathematics festival and BrainBashers.