SOLUTION: Ms.Ikelyn, I asked a question here: https://www.algebra.com/tutors/students/your-answer.mpl?question=1204433 To which you responded (with a helpful!) lesson about a TWIN probl

Question 1204467: Ms.Ikelyn,
I asked a question here: https://www.algebra.com/tutors/students/your-answer.mpl?question=1204433
To which you responded (with a helpful!) lesson about a TWIN problem. However, I am confused and need help. What is that "shift" term? And can you break it down simpler?
Thank you Ma'am
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

Let us assume these bottles are circles with radius 5cm for simplicity.
The densest possible packing is hexagonal packing for circles, as shown below:

For the first layer, we find that the maximum amount of spheres we can fit on the first layer is circles.
Since the second layer is in between the circles, one can only fit circles. The third layer can fit another circles and so on.
Then, we can build an equilateral triangle and show that every stack increases the width of the area filled by

Given the first layer has a thickness (remember, circle represents bottles) of , the amount of layers that can be fitted is the floor of
or layers.
since first two layers have circles, and there is , means *first two layers have and means we take one more first layer which is
This can be formed into
circles, in your case bottles.
answer: bottles

RELATED QUESTIONS
I posted a problem here:... (answered by greenestamps)

Ms.Ikelyn, for the solution you gave for the problem here:... (answered by math_tutor2020)

How do you write 17! as the difference of two integer perfect squares? Ms.Ikelyn... (answered by ikleyn,math_tutor2020)

Hi, I need help on the question from this, and have a question for Ms.Ikelyn:... (answered by MathLover1,ikleyn)

Hi, This solution makes no sense. Please help!... (answered by mananth)

MathLover1 has a reputation to provide incorrect solutions. Here is one she posted... (answered by ikleyn)

https://www.algebra.com/tutors/students/your-answer.mpl?question=1200558 In this... (answered by ikleyn)

It is possible to factor x^2 - y^2 by the technique of adding in an extra term, and... (answered by ikleyn)

Dear MathTutor, I appreciate your response on the question I asked regarding the... (answered by math_tutor2020)