CSCI1540 Fundamental Computing with C++, Fall 2024/25 
Department of Computer Science and Engineering, The Chinese University of Hong Kong 
Copyright © 2024 CSE, CUHK Page 1 of 2 
Due: 23:59, Thu 17 Oct 2024 File name: kaprekar.cpp Full marks: 100 
Introduction 
The objective of this assignment is to master the use of selective and nested repetitive control flow. 
You will write nested loops to look for Kaprekar numbers. 
A Kaprekar number is a positive integer    if the digits of the square   
2
 can be split into two parts 
that add up to   , where the part formed from the low-order (rightmost) digits of   
2
 must be nonzero
 (although leading zeroes are allowed in the part). For example, 45 is a Kaprekar number, 
because 45
2 = 2025 can be split into two parts 20 and 25, with 20 + 25 = 45. As another example, 
999 is also a Kaprekar number, because 999
2 = 998001 and 998 + 001 = 999. (Note the loworder
 part 001 includes leading zeroes.) However, 31 is not a Kaprekar number, because all three 
possible splits of 31
2 = 961 are no good (96 + 1 ≠ 31, 9 + 61 ≠ 31, and 0 + 961 ≠ 31). 
Program Specification 
The program shall ask for two user inputs    and   . They are assumed to be always integers. You are 
required to use the data type long long instead of int for all integer variables in this assignment, 
because a square can easily go overflow with (that is, larger than the upper bound of) the int type. 
1. The program first prompts the user to enter an integer   . When    is not positive, you shall 
display a warning message and ask for another input, until    is positive. Your program shall look 
for Kaprekar number(s) greater than or equal to   . 
2. Then prompt the user to enter how many Kaprekar numbers the user is looking for. When this 
input    is not positive, display a warning message and ask for another input, until    is positive. 
3. After validating inputs    and   , repeatedly test   ,    + 1,    + 2,    + 3, … to check whether it is a 
Kaprekar number. If so, print out the square and the split of the two parts. (See the upcoming 
Sample Runs section for the printing format.) Repeat these checks until    Kaprekar numbers are 
found and printed. Then program execution ends. 
➢ To check whether a number    is a Kaprekar number, you progressively check all possible 
splits of   
2
. E.g., let    = 345 and hence   
2 = 11**25. The first split to check is 11**2 and 
5; the next split is 11** and 25; the next split is 119 and 025; and so on. 
Note: In this assignment, you are not allowed to: (1) use any functions in the <cmath> library, (2) 
write any functions other than main(), and (3) use any arrays/vectors (which are not yet taught). 
Sample Runs 
In the following sample runs, the blue text is user input and the other text is the program printout. 
You can try the provided sample program for other input. Your program output should be exactly the 
same as the sample program (same text, symbols, letter case, spacings, etc.). Note that there is a 
space after the ‘:’ and ‘?’ in the program printout. CSCI1540 Fundamental Computing with C++, Fall 2024/25 
Department of Computer Science and Engineering, The Chinese University of Hong Kong 
Copyright © 2024 CSE, CUHK Page 2 of 2 
Enter an integer: 40↵ 
How many Kaprekar numbers? 3↵ 
45^2 = 2025 
20 + 25 = 45 
55^2 = 3025 
30 + 25 = 55 
99^2 = 9801 
98 + 1 = 99 
 
Enter an integer: -23↵ 
Input must be +ve! Enter again. 
Enter an integer: -1↵ 
Input must be +ve! Enter again. 
Enter an integer: 0↵ 
Input must be +ve! Enter again. 
Enter an integer: 200↵ 
How many Kaprekar numbers? 0↵ 
Input must be +ve! Enter again. 
How many Kaprekar numbers? 0↵ 
Input must be +ve! Enter again. 
How many Kaprekar numbers? -777↵ 
Input must be +ve! Enter again. 
How many Kaprekar numbers? 5↵ 
297^2 = 88209 
88 + 209 = 297 
703^2 = 494209 
494 + 209 = 703 
999^2 = 998001 
998 + 1 = 999 
2223^2 = 4941729 
494 + 1729 = 2223 
2728^2 = 7441984 
744 + 1984 = 2728 
Submission and Marking 
• Your program file name shall be kaprekar.cpp. Submit the file in Blackboard 
(https://blackboard.cuhk.edu.hk/). 
• Insert your name, student ID, and e-mail as comments at the beginning of your source file. 
• You can submit your assignment multiple times. Only the latest submission counts. 
• Your program should be free of compilation errors and warnings. 
• Your program should include suitable comments as documentation. 
• Do NOT share your work to others and do NOT plagiarize. Both senders and plagiarists shall be 
penalized. 

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