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# Tag Archives: summation problems

## Total Number of Triangles Puzzle

How many triangles are there in the figure below?

Solution to this Geometry Triangle Puzzle problem is given in the video below!

## Total Number of Rectangles Puzzle

How many rectangles are there in the figure below?

Solution to this Geometry Rectangle Puzzle is given in the video below!

## Total Number of Upright SQUARES in a Square

How many upright Squares are there in the following square?

The key is to understand vertices of any given upright square and a diagonal line of the largest square to see how many translations of that given upright square you can have. As such, there is a summation-derived FORMULA you can actually use for any largest size square to find the total number of possible upright squares contained within it!

Solution to this Geometry Square Puzzle is given in the video below!

## Total Number of Upright RECTANGLES in a Square (or Rectangle)

How many upright Rectangles are there in the following square?

The key is to understand vertices of any given upright rectangle to see how many unique translations of that rectangle are possible. As such, there is actually a summation-derived FORMULA you can utilize for the largest square or rectangle of any size to find the total number of possible upright rectangles within it!

Solution to this Geometry Rectangle Puzzle is given in the video below!

## Total Number of Upright SQUARES in a Rectangle

How many upright Squares are there in the following rectangle?

The key is to understand vertices of any given upright square to see how many translations of that given square you can have. As such, there is a summation-related FORMULA you can actually derive for any size rectangle to find the total number of possible upright squares contained within it!

Solution to this Square Rectangle Geometry Puzzle is given in the video below!

## Total Number of Upright & Tilted SQUARES in a Square

How many upright and tilted Squares are there in the following square?

The key is to use vertices of any given largest square to see how many translations of a given smaller square you can have. As such, there is a summation-derived FORMULA you can actually use for any size square to find the total number of possible upright and tilted squares contained within it!

Solution to this Square Geometry Puzzle example is given in the video below!

## Total Number of Upright & Tilted SQUARES in a Rectangle

How many upright and tilted Squares are there in the following rectangle?

The key is to use vertices of any given rectangle to see how many translations of a given square you can have. As such, there is a summation-derived FORMULA you can actually use for any size rectangle to find the total number of possible upright and tilted squares contained within it!

Solution to this Rectangle Geometry Puzzle example problem is given in the video below!