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Check if a number is a mystery number

The "Mystery Number" problem is a fun and interesting mathematical puzzle. Given a positive integer, we want to determine if it is a mystery number and find the two positive integers whose sum is equal to the given number, and their reverse numbers are equal to each other.

Problem Statement

A mystery number is a positive integer N that can be expressed as the sum of two positive integers X and Y (X > 0, Y > 0) such that the reverse of X is equal to Y, and vice versa. We need to check whether a given number N is a mystery number and, if so, find the values of X and Y.

Explanation with Examples

  1. Let's take the number 33 as an example:

    • We start with X = 1 and Y = 32 (33 - 1).
    • The reverse of 1 is 1, which is equal to Y. So, 33 is a mystery number with X = 1 and Y = 32.

  2. Consider the number 948:

    • We start with X = 1 and Y = 947 (948 - 1).
    • The reverse of 1 is 1, but it is not equal to Y (which is 749). So, we increment X to 2 and set Y = 946 (948 - 2).
    • The reverse of 2 is 2, which is not equal to Y. We continue this process until we find that X = 177 and Y = 771.
    • The reverse of 177 is 771, which is equal to Y. Therefore, 948 is a mystery number with X = 177 and Y = 771.

Pseudocode and Algorithm

Let's outline the pseudocode for solving the mystery number problem:

reverse_num(number):
    result = 0
    while number is not 0:
        result = result * 10 + (number % 10)
        number = number / 10
    return result

is_mystery_no(number):
    status = 0
    x = 1
    y = 0
    counter = 1
    while counter <= (number / 2) and status is 0:
        x = counter
        y = number - counter
        if x % 10 is not 0 and y % 10 is not 0:
            if reverse_num(x) is equal to y:
                status = 1
        counter = counter + 1
    if status is 1:
        print "[number] Is Mystery Number Of (x, y)"
    else:
        print "[number] Is Not Mystery Number"

Explanation

  • The reverse_num function takes an integer as input and returns its reverse number. For example, reverse_num(123) returns 321.

  • The is_mystery_no function checks whether the given number is a mystery number or not. It initializes status to 0, which will be set to 1 if we find a valid pair (x, y). It uses a counter to iterate through possible values of x, and calculates y accordingly.

  • Inside the loop, it checks whether both x and y are non-zero digits (last digit is not zero) to ensure that they are positive integers. Then, it checks whether the reverse of x is equal to y.

  • If a valid pair (x, y) is found, it sets status to 1 and breaks out of the loop. Finally, it prints the result indicating whether the given number is a mystery number or not, along with the values of x and y if applicable.

Code Solution

Here given code implementation process.

// C program
// Check if a number is a mystery number

#include <stdio.h>

int reverse_num(int number)
{
	int result = 0;
	while (number != 0)
	{
		result = result * 10 + (number % 10);
		number = number / 10;
	}
	//returning the reversal of number
	return result;
}

//Check whether given number is Mystery Number or not
void is_mystery_no(int number)
{
	int status = 0;
	int x = 1;
	int y = 0;
	int counter = 1;
	while (counter <= (number / 2) && status == 0)
	{
		x = counter;
		y = number - counter;
		// Note that x + y is always equal to given number
		// Check whether, given number are last digit is zero or not
		if (x % 10 != 0 && y % 10 != 0)
		{
			if (reverse_num(x) == y)
			{
				//When both numbers are equal
				status = 1;
			}
		}
		counter++;
	}
	if (status == 1)
	{
		printf("\n [%d] Is Mystery Number Of (%d,%d)", number, x, y);
	}
	else
	{
		printf("\n [%d] Is Not Mystery Number", number);
	}
}

int main()
{
	//Test case
	is_mystery_no(33);
	is_mystery_no(948);
	is_mystery_no(44);
	is_mystery_no(123);
	is_mystery_no(143);
	is_mystery_no(154);
	return 0;
}

Output

 [33] Is Mystery Number Of (12,21)
 [948] Is Mystery Number Of (177,771)
 [44] Is Mystery Number Of (13,31)
 [123] Is Not Mystery Number
 [143] Is Mystery Number Of (49,94)
 [154] Is Mystery Number Of (59,95)
// Java program 
// Check if a number is a mystery number

class MysteryNo
{
	public int reverse_num(int number)
	{
		int result = 0;
		while (number != 0)
		{
			result = result * 10 + (number % 10);
			number = number / 10;
		}
		//returning the reversal of number
		return result;
	}
	//Check whether given number is Mystery Number or not
	public void is_mystery_no(int number)
	{
		boolean status = false;
		int x = 1;
		int y = 0;
		int counter = 1;
		while (counter <= (number / 2) && status == false)
		{
			x = counter;
			y = number - counter;
			// Note that x + y is always equal to given number
			// Check whether, given number are last digit is zero or not
			if (x % 10 != 0 && y % 10 != 0)
			{
				if (reverse_num(x) == y)
				{
					//When both numbers are equal
					status = true;
				}
			}
			counter++;
		}
		if (status == true)
		{
			System.out.print("\n [" + number + "] Is Mystery Number Of (" + x + "," + y + ")");
		}
		else
		{
			System.out.print("\n [" + number + "] Is Not Mystery Number");
		}
	}
	public static void main(String[] args)
	{
		MysteryNo obj = new MysteryNo();
		//Test case
		obj.is_mystery_no(33);
		obj.is_mystery_no(948);
		obj.is_mystery_no(44);
		obj.is_mystery_no(123);
		obj.is_mystery_no(143);
		obj.is_mystery_no(154);
	}
}

Output

 [33] Is Mystery Number Of (12,21)
 [948] Is Mystery Number Of (177,771)
 [44] Is Mystery Number Of (13,31)
 [123] Is Not Mystery Number
 [143] Is Mystery Number Of (49,94)
 [154] Is Mystery Number Of (59,95)
//Include header file
#include <iostream>
using namespace std;

// C++ program 
// Check if a number is a mystery number

class MysteryNo
{
	public: int reverse_num(int number)
	{
		int result = 0;
		while (number != 0)
		{
			result = result *10 + (number % 10);
			number = number / 10;
		}
		//returning the reversal of number
		return result;
	}
	//Check whether given number is Mystery Number or not
	void is_mystery_no(int number)
	{
		bool status = false;
		int x = 1;
		int y = 0;
		int counter = 1;
		while (counter <= (number / 2) && status == false)
		{
			x = counter;
			y = number - counter;
			// Note that x + y is always equal to given number
			// Check whether, given number are last digit is zero or not
			if (x % 10 != 0 && y % 10 != 0)
			{
				if (this->reverse_num(x) == y)
				{
					//When both numbers are equal
					status = true;
				}
			}
			counter++;
		}
		if (status == true)
		{
			cout << "\n [" << number << "] Is Mystery Number Of (" << x << "," << y << ")";
		}
		else
		{
			cout << "\n [" << number << "] Is Not Mystery Number";
		}
	}
};
int main()
{
	MysteryNo obj = MysteryNo();
	//Test case
	obj.is_mystery_no(33);
	obj.is_mystery_no(948);
	obj.is_mystery_no(44);
	obj.is_mystery_no(123);
	obj.is_mystery_no(143);
	obj.is_mystery_no(154);
	return 0;
}

Output

 [33] Is Mystery Number Of (12,21)
 [948] Is Mystery Number Of (177,771)
 [44] Is Mystery Number Of (13,31)
 [123] Is Not Mystery Number
 [143] Is Mystery Number Of (49,94)
 [154] Is Mystery Number Of (59,95)
//Include namespace system
using System;

// C# program 
// Check if a number is a mystery number

class MysteryNo
{
	public int reverse_num(int number)
	{
		int result = 0;
		while (number != 0)
		{
			result = result * 10 + (number % 10);
			number = number / 10;
		}
		//returning the reversal of number
		return result;
	}
	//Check whether given number is Mystery Number or not
	public void is_mystery_no(int number)
	{
		Boolean status = false;
		int x = 1;
		int y = 0;
		int counter = 1;
		while (counter <= (number / 2) && status == false)
		{
			x = counter;
			y = number - counter;
			// Note that x + y is always equal to given number
			// Check whether, given number are last digit is zero or not
			if (x % 10 != 0 && y % 10 != 0)
			{
				if (reverse_num(x) == y)
				{
					//When both numbers are equal
					status = true;
				}
			}
			counter++;
		}
		if (status == true)
		{
			Console.Write("\n [" + number + "] Is Mystery Number Of (" + x + "," + y + ")");
		}
		else
		{
			Console.Write("\n [" + number + "] Is Not Mystery Number");
		}
	}
	public static void Main(String[] args)
	{
		MysteryNo obj = new MysteryNo();
		//Test case
		obj.is_mystery_no(33);
		obj.is_mystery_no(948);
		obj.is_mystery_no(44);
		obj.is_mystery_no(123);
		obj.is_mystery_no(143);
		obj.is_mystery_no(154);
	}
}

Output

 [33] Is Mystery Number Of (12,21)
 [948] Is Mystery Number Of (177,771)
 [44] Is Mystery Number Of (13,31)
 [123] Is Not Mystery Number
 [143] Is Mystery Number Of (49,94)
 [154] Is Mystery Number Of (59,95)
<?php
// Php program 
// Check if a number is a mystery number
class MysteryNo
{
	public	function reverse_num($number)
	{
		$result = 0;
		while ($number != 0)
		{
			$result = $result * 10 + ($number % 10);
			$number = intval($number / 10);
		}
		//returning the reversal of number
		return $result;
	}
	//Check whether given number is Mystery Number or not
	public	function is_mystery_no($number)
	{
		$status = false;
		$x = 1;
		$y = 0;
		$counter = 1;
		while ($counter <= (intval($number / 2)) && $status == false)
		{
			$x = $counter;
			$y = $number - $counter;
			// Note that x + y is always equal to given number
			// Check whether, given number are last digit is zero or not
			if ($x % 10 != 0 && $y % 10 != 0)
			{
				if ($this->reverse_num($x) == $y)
				{
					//When both numbers are equal
					$status = true;
				}
			}
			$counter++;
		}
		if ($status == true)
		{
			echo "\n [". $number ."] Is Mystery Number Of (". $x .",". $y .")";
		}
		else
		{
			echo "\n [". $number ."] Is Not Mystery Number";
		}
	}
}

function main()
{
	$obj = new MysteryNo();
	//Test case
	$obj->is_mystery_no(33);
	$obj->is_mystery_no(948);
	$obj->is_mystery_no(44);
	$obj->is_mystery_no(123);
	$obj->is_mystery_no(143);
	$obj->is_mystery_no(154);
}
main();

Output

 [33] Is Mystery Number Of (12,21)
 [948] Is Mystery Number Of (177,771)
 [44] Is Mystery Number Of (13,31)
 [123] Is Not Mystery Number
 [143] Is Mystery Number Of (49,94)
 [154] Is Mystery Number Of (59,95)
// Node Js program 
// Check if a number is a mystery number
class MysteryNo
{
	reverse_num(number)
	{
		var result = 0;
		while (number != 0)
		{
			result = result * 10 + (number % 10);
			number = parseInt(number / 10);
		}
		//returning the reversal of number
		return result;
	}
	//Check whether given number is Mystery Number or not
	is_mystery_no(number)
	{
		var status = false;
		var x = 1;
		var y = 0;
		var counter = 1;
		while (counter <= (parseInt(number / 2)) && status == false)
		{
			x = counter;
			y = number - counter;
			// Note that x + y is always equal to given number
			// Check whether, given number are last digit is zero or not
			if (x % 10 != 0 && y % 10 != 0)
			{
				if (this.reverse_num(x) == y)
				{
					//When both numbers are equal
					status = true;
				}
			}
			counter++;
		}
		if (status == true)
		{
			process.stdout.write("\n [" + number + "] Is Mystery Number Of (" + x + "," + y + ")");
		}
		else
		{
			process.stdout.write("\n [" + number + "] Is Not Mystery Number");
		}
	}
}

function main()
{
	var obj = new MysteryNo();
	//Test case
	obj.is_mystery_no(33);
	obj.is_mystery_no(948);
	obj.is_mystery_no(44);
	obj.is_mystery_no(123);
	obj.is_mystery_no(143);
	obj.is_mystery_no(154);
}
main();

Output

 [33] Is Mystery Number Of (12,21)
 [948] Is Mystery Number Of (177,771)
 [44] Is Mystery Number Of (13,31)
 [123] Is Not Mystery Number
 [143] Is Mystery Number Of (49,94)
 [154] Is Mystery Number Of (59,95)
#  Python 3 program 
#  Check if a number is a mystery number

class MysteryNo :
	def reverse_num(self, number) :
		result = 0
		while (number != 0) :
			result = result * 10 + (number % 10)
			number = int(number / 10)
		
		# returning the reversal of number
		return result
	
	# Check whether given number is Mystery Number or not
	def is_mystery_no(self, number) :
		status = False
		x = 1
		y = 0
		counter = 1
		while (counter <= (int(number / 2)) and status == False) :
			x = counter
			y = number - counter
			#  Note that x + y is always equal to given number
			#  Check whether, given number are last digit is zero or not
			if (x % 10 != 0 and y % 10 != 0) :
				if (self.reverse_num(x) == y) :
					# When both numbers are equal
					status = True
				
			
			counter += 1
		
		if (status == True) :
			print("\n [", number ,"] Is Mystery Number Of (", x ,",", y ,")", end = "")
		else :
			print("\n [", number ,"] Is Not Mystery Number", end = "")
		
	

def main() :
	obj = MysteryNo()
	# Test case
	obj.is_mystery_no(33)
	obj.is_mystery_no(948)
	obj.is_mystery_no(44)
	obj.is_mystery_no(123)
	obj.is_mystery_no(143)
	obj.is_mystery_no(154)

if __name__ == "__main__": main()

Output

 [ 33 ] Is Mystery Number Of ( 12 , 21 )
 [ 948 ] Is Mystery Number Of ( 177 , 771 )
 [ 44 ] Is Mystery Number Of ( 13 , 31 )
 [ 123 ] Is Not Mystery Number
 [ 143 ] Is Mystery Number Of ( 49 , 94 )
 [ 154 ] Is Mystery Number Of ( 59 , 95 )
#  Ruby program 
#  Check if a number is a mystery number

class MysteryNo 
	def reverse_num(number) 
		result = 0
		while (number != 0) 
			result = result * 10 + (number % 10)
			number = number / 10
		end

		# returning the reversal of number
		return result
	end

	# Check whether given number is Mystery Number or not
	def is_mystery_no(number) 
		status = false
		x = 1
		y = 0
		counter = 1
		while (counter <= (number / 2) && status == false) 
			x = counter
			y = number - counter
			#  Note that x + y is always equal to given number
			#  Check whether, given number are last digit is zero or not
			if (x % 10 != 0 && y % 10 != 0) 
				if (self.reverse_num(x) == y) 
					# When both numbers are equal
					status = true
				end

			end

			counter += 1
		end

		if (status == true) 
			print("\n [", number ,"] Is Mystery Number Of (", x ,",", y ,")")
		else 
			print("\n [", number ,"] Is Not Mystery Number")
		end

	end

end

def main() 
	obj = MysteryNo.new()
	# Test case
	obj.is_mystery_no(33)
	obj.is_mystery_no(948)
	obj.is_mystery_no(44)
	obj.is_mystery_no(123)
	obj.is_mystery_no(143)
	obj.is_mystery_no(154)
end

main()

Output

 [33] Is Mystery Number Of (12,21)
 [948] Is Mystery Number Of (177,771)
 [44] Is Mystery Number Of (13,31)
 [123] Is Not Mystery Number
 [143] Is Mystery Number Of (49,94)
 [154] Is Mystery Number Of (59,95)
// Scala program 
// Check if a number is a mystery number

class MysteryNo
{
	def reverse_num(n: Int): Int = {
      	var number: Int = n;
		var result: Int = 0;
		while (number != 0)
		{
			result = result * 10 + (number % 10);
			number = (number / 10).toInt;
		}
		//returning the reversal of number
		return result;
	}
	//Check whether given number is Mystery Number or not
	def is_mystery_no(number: Int): Unit = {
		var status: Boolean = false;
		var x: Int = 1;
		var y: Int = 0;
		var counter: Int = 1;
		while (counter <= ((number / 2).toInt) && status == false)
		{
			x = counter;
			y = number - counter;
			// Note that x + y is always equal to given number
			// Check whether, given number are last digit is zero or not
			if (x % 10 != 0 && y % 10 != 0)
			{
				if (reverse_num(x) == y)
				{
					//When both numbers are equal
					status = true;
				}
			}
			counter += 1;
		}
		if (status == true)
		{
			print("\n [" + number + "] Is Mystery Number Of (" + x + "," + y + ")");
		}
		else
		{
			print("\n [" + number + "] Is Not Mystery Number");
		}
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var obj: MysteryNo = new MysteryNo();
		//Test case
		obj.is_mystery_no(33);
		obj.is_mystery_no(948);
		obj.is_mystery_no(44);
		obj.is_mystery_no(123);
		obj.is_mystery_no(143);
		obj.is_mystery_no(154);
	}
}

Output

 [33] Is Mystery Number Of (12,21)
 [948] Is Mystery Number Of (177,771)
 [44] Is Mystery Number Of (13,31)
 [123] Is Not Mystery Number
 [143] Is Mystery Number Of (49,94)
 [154] Is Mystery Number Of (59,95)
// Swift 4 program 
// Check if a number is a mystery number
class MysteryNo
{
	func reverse_num(_ n: Int) -> Int
	{
      	var number: Int = n;
		var result: Int = 0;
		while (number != 0)
		{
			result = result * 10 + (number % 10);
			number = number / 10;
		}
		//returning the reversal of number
		return result;
	}
	//Check whether given number is Mystery Number or not
	func is_mystery_no(_ number: Int)
	{
		var status: Bool = false;
		var x: Int = 1;
		var y: Int = 0;
		var counter: Int = 1;
		while (counter <= (number / 2) && status == false)
		{
			x = counter;
			y = number - counter;
			// Note that x + y is always equal to given number
			// Check whether, given number are last digit is zero or not
			if (x % 10 != 0 && y % 10 != 0)
			{
				if (self.reverse_num(x) == y)
				{
					//When both numbers are equal
					status = true;
				}
			}
			counter += 1;
		}
		if (status == true)
		{
			print("\n [", number ,"]Is Mystery Number Of (", x ,",", y ,")", terminator: "");
		}
		else
		{
			print("\n [", number ,"]Is Not Mystery Number", terminator: "");
		}
	}
}
func main()
{
	let obj: MysteryNo = MysteryNo();
	//Test case
	obj.is_mystery_no(33);
	obj.is_mystery_no(948);
	obj.is_mystery_no(44);
	obj.is_mystery_no(123);
	obj.is_mystery_no(143);
	obj.is_mystery_no(154);
}
main();

Output

 [ 33 ]Is Mystery Number Of ( 12 , 21 )
 [ 948 ]Is Mystery Number Of ( 177 , 771 )
 [ 44 ]Is Mystery Number Of ( 13 , 31 )
 [ 123 ]Is Not Mystery Number
 [ 143 ]Is Mystery Number Of ( 49 , 94 )
 [ 154 ]Is Mystery Number Of ( 59 , 95 )

Time Complexity

The time complexity of the algorithm mainly depends on the reverse_num function, which has a time complexity of O(log n), where n is the number of digits in the input number. The is_mystery_no function has a loop that runs up to number/2 times, so its time complexity is O(number). Therefore, the overall time complexity of the code is O(number * log n), where n is the number of digits in the input number.

Output Explanation

The given C program calls the is_mystery_no function for several test cases:

  1. is_mystery_no(33): The function finds that 33 is a mystery number with x = 12 and y = 21. So, it prints "[33] Is Mystery Number Of (12, 21)".

  2. is_mystery_no(948): The function finds that 948 is a mystery number with x = 177 and y = 771. So, it prints "[948] Is Mystery Number Of (177, 771)".

  3. is_mystery_no(44): The function finds that 44 is a mystery number with x = 13 and y = 31. So, it prints "[44] Is Mystery Number Of (13, 31)".

  4. is_mystery_no(123): The function doesn't find a valid pair (x, y) for 123, so it prints "[123] Is Not Mystery Number".

  5. is_mystery_no(143): The function finds that 143 is a mystery number with x = 49 and y = 94. So, it prints "[143] Is Mystery Number Of (49, 94)".

  6. is_mystery_no(154): The function finds that 154 is a mystery number with x = 59 and y = 95. So, it prints "[154] Is Mystery Number Of (59, 95)".

The output confirms whether each test case is a mystery number or not, and if it is, it provides the corresponding values of x and y.

Last updated on by Kalkicode




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