Open and Shut
How it works
Imagine you have a grid like the one shown above. Each square in the grid can be either open or shut, and you get to decide which squares are open and which are shut. Can you figure out which squares to shut so that for each row and each column, the numbers in the open squares add up to the target for that row or column? Can you do it without guessing?
In this activity, students explore a variety of different puzzles like the one shown above, with different grids and different row / column targets. Some of these puzzles are possible to solve, and some are impossible! Students are encouraged to find strategies to solve the puzzles that are possible without guessing.
Why we like this activity
It’s fun! Students enjoy trying to solve the puzzles.
It helps students to develop numerical reasoning.
It helps students to develop logical reasoning.
It requires students to engage in mathematical habits of mind:
Finding and using strategies to solve the puzzles efficiently (without guessing)
Using logic and understanding and explaining when trying to determine which puzzles are impossible
It has a low floor and a high ceiling: Students can start solving puzzles by trial and error, but as the puzzles get more challenging, more careful strategizing is required!
This activity was adapted from the Julia Robinson Mathematics Festival's activity Cover Up.