Border Tiles Puzzle

Puzzle Board

The border tiles is a traditional problem in which you are asked to write an expression to calculate the number of tiles needed to border a given pool. The shape of the pool is usually a square or a rectangle, but any shape can be used as a pool too!

Hints

For younger students, starting with a square pool of 1 by 1 and enlarging the pool one square at a time can help to find the general pattern.

For the rectangular pool, the following questions may be helpful:

• What are the dimensions of the pool? What is its area?
• What are the dimensions of the area enclosed by the border tiles? Its area?
• What does the difference between areas represent?
• For an n x m pool, what are the dimensions of the area enclosed by the border tiles?

Solution

Square Pool

The beauty of this problem is the endless ways of analyzing the shape. Here are a few different ways to look at a 5 by 5 square pool.

Rectangular Pool

Rectangular Pools are very similar to square pools. The general formula for an n x m rectangle is $2n+ 2m+ 4$.

For a 12 x 16 pool, the number of red tiles will be 60.

More on the Border Tiles Puzzle

You may continue to study other shapes to solve the border problems. Here is an L shape pool example;

Visit the Visual Patterns Tasks Page to practice exploring and creating patterns.

Next

If you like this puzzle, try this one!