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#The riddle can be found at https://fivethirtyeight.com/features/how-long-will-it-take-to-blow-out-the-birthday-candles/

tests = 10000000
blows <- rep(0,tests)
i = 1

while (i <=tests) {
  candles = 30
  
  while (candles > 0) {

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# Cameron Pfiffer
# July 31st, 2017
# Julia Does Numbers 2: The Mathening

# See the link below for information about the challenge.
# https://fivethirtyeight.com/features/pick-a-number-any-number/

#=
From Itay Bavly, a chain-link number problem:

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# Misc functions for conservation biology stats in R.

shannon <- function (x) {
  proportion_x = x/sum(x)
  print(proportion_x)
  print(log(proportion_x))
  print(proportion_x * log(proportion_x))
  print(sum(proportion_x * log(proportion_x)))
  return(-sum(proportion_x*log(proportion_x)))
}

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# From Keith Wynroe, a battle for the tokens:
#
# You have one token, and I have two tokens. Naturally, we both crave more tokens, so we play a game of skill that unfolds over a number of rounds in which the winner of each round gets to steal one token from the loser. The game itself ends when one of us is out of tokens — that person loses. Suppose that you’re better than me at this game and that you win each round two-thirds of the time and lose one-third of the time.
#
# What is your probability of winning the game?

@everywhere function play_game()
    p1 = 2
    p2 = 1
    play = true

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Keybase proof

I hereby claim:

• I am cpfiffer on github.
• I am cpfiffer (https://keybase.io/cpfiffer) on keybase.
• I have a public key ASBuOyV4zsOUIxWVtBtAh0aRwqkKu25BwWPjUIxgfL8R4go

To claim this, I am signing this object:

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module P21 (properDivisors, sumDivisors, sumAmicable, isAmicable, amicableList) where



properDivisors :: Int -> [Int]
properDivisors x = [xs | xs <- [1..x-1], x `mod` xs == 0]

sumDivisors :: Int -> Int
sumDivisors x = sum $ properDivisors x

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using CmdStan, DynamicHMC
using StatsPlots, Random, MCMCDiagnostics
using Revise
using Turing, AdvancedHMC; const AHMC = AdvancedHMC
Random.seed!(1239911)

ProjDir = @__DIR__
cd(ProjDir)

Nsamples = 2000

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using CmdStan, StatsPlots, Random, MCMCDiagnostics

Random.seed!(12395391)

ProjDir = @__DIR__
cd(ProjDir)

berstanmodel = "
data { 
  int<lower=0> N; 

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using MCMCChains

function sim(nsamples)
    cnt = 0
    for i in 1:1000
        chn = Chains(randn(nsamples,1,1))
        ess = describe(chn)[1].df[:ess][1]
        ess > nsamples ? cnt+=1 : nothing 
    end 
    return cnt 

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using Turing
using CSVFiles
using DataFrames
using Dates
using StatsPlots

# The TV syntax allows sampling to be type-stable.
@model garch(r, ::Type{TV}=Vector{Float64}) where {TV} = begin
    T = length(r)