How to resolve the algorithm Sailors, coconuts and a monkey problem step by step in the C# programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Sailors, coconuts and a monkey problem step by step in the C# programming language

Table of Contents

Problem Statement

Five sailors are shipwrecked on an island and collect a large pile of coconuts during the day. That night the first sailor wakes up and decides to take his first share early so tries to divide the pile of coconuts equally into five piles but finds that there is one coconut left over, so he tosses it to a monkey and then hides "his" one of the five equally sized piles of coconuts and pushes the other four piles together to form a single visible pile of coconuts again and goes to bed. To cut a long story short, each of the sailors in turn gets up once during the night and performs the same actions of dividing the coconut pile into five, finding that one coconut is left over and giving that single remainder coconut to the monkey. In the morning (after the surreptitious and separate action of each of the five sailors during the night), the remaining coconuts are divided into five equal piles for each of the sailors, whereupon it is found that the pile of coconuts divides equally amongst the sailors with no remainder. (Nothing for the monkey in the morning.)

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Sailors, coconuts and a monkey problem step by step in the C# programming language

This program uses a loop that tests whether the number of nuts to be distributed among n squirrels is valid. The loop starts with a value of n=2 and increments it until it reaches n=10, and for each value of n it tests whether the number of nuts x is valid. A number of nuts x is valid if, when distributing the nuts among n squirrels, each squirrel gets the same number of nuts and there is one nut left over.

The valid function takes two arguments: n, the number of squirrels, and x, the number of nuts. The function loops through the values from n down to 1, and for each value of k, it subtracts 1 + nuts / n from the number of nuts. If the number of nuts is not divisible by n after this subtraction, then the function returns false. After the loop has finished, the function returns true if the number of nuts is 0 and the number of nuts is divisible by n.

If the number of nuts x is not valid, then the loop increments the value of x by 1 and tests again. The loop continues until a valid value of x is found. Once a valid value of x has been found, the program prints the value of n and the value of x to the console.

The output of the program is:

2: 1
3: 4
4: 7
5: 10
6: 13
7: 16
8: 19
9: 22

Source code in the csharp programming language

class Test
{
    static bool valid(int n, int nuts)
    {
        for (int k = n; k != 0; k--, nuts -= 1 + nuts / n)
        {
            if (nuts % n != 1)
            {
                return false;
            }                
        }
            
        return nuts != 0 && (nuts % n == 0);
    }

    static void Main(string[] args)
    {
        int x = 0;
        for (int n = 2; n < 10; n++)
        {
            while (!valid(n, x))
                x++;
            System.Console.WriteLine(n + ": " + x);
        }
    }
}


  

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