Cell Reproduction

Python Puzzles

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You are conducting a controlled experiment where you have a single cell. After a certain and reoccurring amount of time, the cell has a 2/5 chance of dying, 2/5 chance of being idle, and a 1/5 chance of replicating. After a replication, each cell has the same amount of probability.

Given 1 million trials, what is the maximum number of cells produced?

I routinely get around 75 cells produced, given 1 million trials.

The probability of a trial creating 10 or more cells is only 2%. Given the chart below, you can see how the probability dramatically decreases once the trial begins.

import random
import matplotlib.pyplot as plt
import pandas as pd

result = []

for _ in range(1_000_000):    
    cell = []
    while True in cell:        
        for x in range(len(cell)):
            # randomly select a number between 1 and 5
            random_num = random.randint(1,5)
            # if the cell is alive and the number is 4 or 5, it dies
            if cell[x] == True and random_num in (4,5):
                cell[x] = False
            # if the cell is alive and the number is 3, it reproduces and a new cell is born
            elif cell[x] == True and random_num == 3:        
    # add the final count of cells to the result list

# print the maximum number of cells in any iteration

# create a pandas series and plot the distribution of cell counts
df = pd.Series(result)
df = df.value_counts()

plt.plot(df.index, df.values)
plt.title('Distribution of Cell Count')
plt.xlabel('Cell Count')