How to calculate number of paper folds to get thickness equal to distance to the moon?

I wanted to try how a programming exercise would translate to a blog post.

I opened Brilliant.com and the first exercise was a puzzle of folding paper. I decided to solve it using Julia language.

How thick is a sheet of printer paper?

For this exercise, let's assume 0.097mm to 0.1mm depending on the "weight" of the paper.

# define known variables
building = 828             # units: m -- Burj Khalifa building
moon = 391000000     # units: m; distance to the moon
sheet = 0.1 / 1000        # unit: m -- thickness of 100 sheets is 1 cm

function fold(initial, desired)

folds = 0                                              # initial number of folds

achieved = initial                                # initial thickness

results = []

while true

achieved = achieved * 2               # fold paper

if achieved >= desired break end # check if time to exit the loop

push!(results, achieved)               # add to results

folds = folds + 1                           # increment

end

return results 

end 

results = fold(sheet, moon)                         # replace moon with building
folds = size(results)[1]                               # size is a tuple, get first element
thickness = results[folds] /1_000_000
print("We used $folds to get $thickness thousand km.")
println()
data = results ./ 1000.0                               # data need to be Array{Float64, 1}, in km
increments = size(results)[1]

using Plots

using PlutoUI

How to create a slider in Julia?

I use that slider to show me the progression of thickness from 1 fold to as many as it takes.

@bind slider_ui Slider(1:increments) # one widget per cell

How to create a drop-down menu in Julia?

@bind plot_type Select(["scatter","line","bar"])

How to draw a simple diagram to visualize the data?

 

plot(

data[1:slider_ui], 

seriestype=Symbol(plot_type), 

title="x=$slider_ui folds, y=km, $plot_type plot"

)

 

So, what is the number of folds to get to the moon?

Only 42 folds will take us to the moon and a bit further!