Find the Number of Lychrel Numbers Below Ten-Thousand

How many Lychrel numbers are there below ten-thousand?

Write a C++ program to find this answer. You need to design a function long long reverseNumber(long long) to reverse a number; a function bool isPalindrome(long long) to check whether the number is palindrome; and a function bool isLychrel(long long) to check whether the number is a Lychrel Number.

Answer:

The number of Lychrel numbers below ten-thousand is 249.

In the provided C++ program, we iterate through numbers from 1 to 9999 and count the number of Lychrel numbers using the isLychrel function. The final count is then displayed as the output. It is essential to understand the three functions used in this program:

Functions:

reverseNumber: This function takes a number as input and reverses its digits. It performs the operation of reversing the number by utilizing a while loop in combination with basic arithmetic.

isPalindrome: This function checks whether a number is a palindrome by comparing the original number with its reversed version. It calls the reverseNumber function to reverse the number and then checks for equality.

isLychrel: This function checks whether a number is a Lychrel number. It repeats the process of adding the number to its reverse until either a palindrome is found or the maximum number of iterations (50) is reached. If a palindrome is found, the function returns false; otherwise, it returns true.

By utilizing these three functions efficiently in the main function, we successfully determine the count of Lychrel numbers below ten-thousand. The comprehensive use of for loops and conditional statements ensures that each number is evaluated accurately.