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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!

World’s HARDEST Easy Geometry problem example question

The following triangle, , shows angle measures in the base angles A and C, as well as line segments  , and . Find the measure of angle AED, that is, .

Note: Do not use Trigonometry or Calculus to solve this problem

Solution to this World’s Hardest Easy Geometry practice problem is provided in the video below!

Albert Einstein’s Fish word puzzle

The Englishman lives in the red house.

The Swede keeps dogs.

The Dane drinks tea.

The green house is just to the left of the white one.

The owner of the green house drinks coffee.

The Pall Mall smoker keeps birds.

The owner of the yellow house smokes Dunhills.

The man in the center house drinks milk.

The Norwegian lives in the first house.

The Blend smoker has a neighbor who keeps cats.

The man who smokes Blue Masters drinks bier.

The man who keeps horses lives next to the Dunhill smoker.

The German smokes Prince.

The Norwegian lives next to the blue house.

The Blend smoker has a neighbor who drinks water.

The question to be answered is: Who keeps fish?

Solution to this Puzzle practice problem is provided in the video below!

Shaded Area in a Square puzzle example question

In a unit square ABCD, point A is joined to the midpoint of BC, point B is joined to the midpoint of CD, point C is joined to the midpoint of DA, and point D is joined to the midpoint of AB. Find the area of the shaded region.

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

Shaded Area in a Square puzzle example problem

In a unit square ABCD, M is a midpoint of AD, and AC is a diagonal. Find the area of the shaded regions.

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

Shaded Area in a Square puzzle example

In the unit square ABCD, M is the midpoint and AC and BD are diagonals. Find the area of the shaded region.

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

Shaded Area in a Square puzzle example question

In the following unit square ABCD, M is the midpoint and BD is a diagonal. Find the area of the shaded region.

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

Shaded Area in a Square puzzle TRIGONOMETRY example problem

A square with side 1 is rotated around one vertex by an angle  , where

and

.

Find the area of the shaded region.

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

Shaded Area in a Rectangle puzzle example

In the following rectangle, an isosceles triangle is drawn. Find the area of the shaded region.

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

Shaded Area in a Rectangle puzzle example question

In the following rectangle below, find the area of the shaded region.

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

Water Jug puzzle question

You have 2 water jugs. One jug can be completely filled with 3 gallons of water, and the other jug can be completely filled with 5 gallons of water. You need 4 gallons of water. How would you proceed?

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

Eight Balls Placed on a Balancing Weight Scale puzzle example question

You have 8 balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. How can you find the ball that is heavier by using a balance and only two weighings?

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