A google and amazon interview question with a really clever solution

The video explores the probability of forming a triangle by randomly cutting a stick at two points. It introduces Viviani's theorem, which states that the sum of perpendicular distances from any interior point to the sides of an equilateral triangle equals the triangle's height. This theorem is applied to the stick problem, showing that only one of four possible regions allows for a triangle to be formed, resulting in a 25% probability. The video concludes with a practical application of this geometric concept.

What is the main problem discussed in the first section of the video?

• Determining the odds of forming a triangle from three pieces

• Understanding the properties of a right triangle

• Calculating the area of a triangle

• Finding the perimeter of an equilateral triangle

According to Viviani's theorem, what is true for any point inside an equilateral triangle?

• The sum of the angles is always 180 degrees

• The sum of the perpendicular distances to the sides equals the height

• The area of the triangle is constant

• The perimeter of the triangle is constant

How does Viviani's theorem help in solving the stick problem?

• It relates the interior points of a triangle to possible cuts on the stick

• It provides a method to measure the stick's length

• It helps in calculating the area of the stick

• It determines the color of the stick

What condition must be met for three pieces of a stick to form a triangle?

• The pieces must be longer than the original stick

• The pieces must form a right angle

• All pieces must be of equal length

• The longest piece must be shorter than the sum of the other two

What is the probability that three randomly cut pieces of a stick can form a triangle?

• 25%

• 75%

• 33%

• 50%