Solving the Monkey Peach Problem with Python

1 Problem

On the beach, there is a pile of peaches, and five monkeys come to share them. The first monkey divides the pile into five equal parts, but there is one left over. This monkey throws the extra one into the sea and takes one part. The second monkey divides the remaining peaches into five equal parts, and again there is one left over; it also throws the extra one into the sea and takes one part. The third, fourth, and fifth monkeys do the same. The question is, what is the minimum number of peaches that were originally on the beach?

2 Method

(1) To find the minimum number of peaches, the fewer peaches left on the shore at the end, the fewer peaches there were originally on the shore.

(2) From the problem, we know that each monkey divides the peaches into five equal parts, and there is always one extra. Inspired by this, we can assume that there are still 4x peaches left on the shore and use a recursive method to solve it.

(3) Now that we have found the mathematical method to solve the problem, we need to convert it into code. First, we define a function and apply the recursive method; finally, we use a while loop.

Code Listing 1

num=int(input("Enter the number of monkeys:"))def fn(n):    if n == num:        return(4*x)    else:        return(fn(n+1)*5/4+1)x=1while 1:    count=0    for i in range(1,num):        if fn(i)%4 == 0 :            count=count+1    if count==num-1:        print("The minimum number of peaches originally on the beach is %d" % int(fn(0)))        break    else:        x=x+1

3 Conclusion

In this tutorial, we first proposed a mathematical method to solve the monkey peach problem, then converted it into a Python problem, utilizing recursive functions and other methods discussed in this blog, successfully demonstrating that these methods are effective through code. There are still many shortcomings and considerations in this approach, and I hope to continuously improve through future learning and practice.