SOLUTION: GREAT PYRAMID OF ORANGES A very bored grocer was stacking oranges one day. She decided to stack them in a triangular pyramid. There was one orange in the top layer, three orang

Question 1161157: GREAT PYRAMID OF ORANGES
A very bored grocer was stacking oranges one day. She decided to stack them in a triangular pyramid. There was one orange in the top layer, three oranges in the second layer, six oranges in the third layer, and so on. Each layer except the top formed an equilateral triangle.
How many oranges would it take her to build a pyramid 50 layers high?

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
.

I will not go into the solution.

I simply recommend you to read these Wikipedia articles, related to the subject

https://en.wikipedia.org/wiki/Triangular_number#:~:text=0%2C%201%2C%203%2C%206,%2C%20630%2C%20666...

https://en.wikipedia.org/wiki/Tetrahedral_number

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

As suggested by tutor @ikleyn, there is a lot of fun mathematics in the patterns involved in solving this problem.

Counting from the top row, the number of oranges in the n-th layer is the n-th triangular number, which is

Those numbers are found in a diagonal of Pascal's Triangle.

The hockey stick identity in Pascal's Triangle (another internet search for you, if you are not familiar with it), tells us that

=

So the number of oranges in the stack of 50 layers is

RELATED QUESTIONS
A very bored grocer was stacking oranges one day. She decided to stack them in a... (answered by venugopalramana)
How Many Oranges? Marjorie, Colleen, and Bob picked oranges together. They were tired... (answered by KMST)
How Many Oranges? Marjorie, Colleen, and Bob picked oranges together. They were tired... (answered by lynnlo)
Diana buys 20 apples at x cents each and 40 oranges at x + 10 cents. She packs them in... (answered by addingup,stanbon,solver91311)
A trader buys 200 oranges at #66 per dozen and 130 oranges at #78 per dozen if 20 oranges (answered by ikleyn)
I have a probability problem. If someone can help me figure out the steps and answer, it (answered by Theo)
RETAIL DISPLAYS You work in a grocery store and you are stacking apples in the shape of... (answered by richard1234)
Hi A grocer buys 20 cases of oranges at $15 a case. Each case has 10kg of oranges. If... (answered by jorel1380,MathTherapy)
Jake buys oranges at 3 for 46�. He sells them at 5 for 80�. In order to make a profit of... (answered by rfer)