Watch the video at this link: https://curiosity.com/videos/6174-numberphile-numberphile/. Then download the Matlab file Kaprekars_operation.m. Test this file with a few random four digit numbers. Note that this script wont work for values less than 1000.

a. Change this file to be a function file that would receive one input of four digits number and would output two values - Output 1: the number the operation reaches (should be Kaprekars constant); Output 2: the number of iterations it took to reach that number. You do not need to submit the function file, but you will need it for your own reference in part b.

b. Write a script that tests the Kaprekars theory for initial values between 1000 and 9998 except for the values 1111, 2222, 3333, ...., 8888. Your script should print the

following:

i. Count of how many initial values were tested.

ii. Count of how many values returned Kaprekars number 6174.

iii. How many of these values took 1 iteration to reach Kaprekars number, along with how many took 2 iterations, 3 iterations, 4 iterations, 5 iterations, 6 iterations, 7 iterations, and more than 8 iterations.

Self-check: for (ii), all values should return 6174. For (iii), all values should take less than 8 iterations.

Kaprekars_operation.m file:

%% Kaprekar's operation (Magic Number Example) Script.

% Watch this video for more explination of the problem:

https://curiosity.com/videos/6174-numberphile-numberphile/

%This script will request the user input a 4-digit number (not all the

%same digit) and from this number will perform calculations to compute the

%constant number 6174 which always follows from the given algorithm.

%Script author: Cody Scharzenberger

%Clear Everything.

clear

close all

clc

%% Request User Input & Verify its Validity.

%Create a boolean variable to store whether the input is valid.

bValidInput = false;

%While the input is not valid, continue asking for user input...

while ~bValidInput

%Request user input.

x = input('Enter a 4 Digit Number (Not All the Same Digit): x = ');

%%% Create an array of the digits of the given number.

%Turn the number into a character array.

xstr = num2str(x);

%Preallocate a variable for storing the digits.

x_digits = zeros(1,length(xstr));

%Store the digits into an array. This will be used to check that not

%all of the digits are the same.

for k = 1:length(xstr)

x_digits(k) = str2double(xstr(k));

end

%%% Determine whether the input is valid.

%(1) Input must have 4 digits,

%(2) Input must not be a single digit repeated four times.

if (length(x_digits) ~= 4) || (sum(x_digits == x_digits(1)) == 4)

fprintf('Invalid Number. Try Again. ')

else

bValidInput = true; %Flag that a valid input has been given.

end

end

%% Perform Algorithm to Compute 6174 from User Input.

%%% Preallocate for a while loop.

%Create a variable to store the values produced by the algorithm.

xs(1) = x; %Set the first value to be the original user input.

%Create a loop variable to determine the number of loop interations.

k = 0;

%Create a boolean flag variable to determine when the algorithm is

%producing the same result.

bMatchFound = false;

%%% Use a while loop to perform the computation.

%Conitnue iterating until the algorithm is producing the same number...

while ~bMatchFound

%Add to the loop variable.

k = k + 1;

%Convert the current number to a string.

xstr = num2str(x);

%Need to add leading zeros if our value has fewer than 4 digits...

xstr = [num2str(zeros(1,4-length(xstr))), xstr]; %IF YOU DON'T HAVE

THIS LINE, SCRIPT WON'T WORK WHEN THE NUMBER HAS THREE REPEATED DIGITS.

%Sort the string into ascending & descending arrays.

xstr_ascend = sort(xstr, 'ascend');

xstr_descend = sort(xstr, 'descend');

%Turn these strings back into double arrays.

x_ascend = str2double(xstr_ascend);

x_descend = str2double(xstr_descend);

%Find the different between these two numbers.

x = x_descend - x_ascend;

%Store this new value into the array tracking the sequence of numbers

%produced by this algorithm.

xs(k+1) = x;

%Check to see if a match has been found. ie, is this number the same

%as the one produced on the previous iteration?

if xs(k) == xs(k+1)

bMatchFound = true; %Switch the flag variable.

end

end

%Compute the number of iterations that were performed.

n = k - 1;

%% Print out the Results.

fprintf(' ')

fprintf('Number of Iterations: n = %0.0f [#] ', n)

fprintf('Magic Sequence: ')

disp(xs(1:end-1))