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 = []
    cell.append(True)
        
    while True in cell:        
        for x in range(len(cell)):
            random_num = random.randint(1,5)
        
            if cell[x] == True and random_num in (4,5):
                cell[x] = False
            elif cell[x] == True and random_num == 3:        
                cell.append(True)
    
    result.append(len(cell))

print(max(result))

df = pd.Series(result)
df = df.value_counts()

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