How to resolve the algorithm Kaprekar numbers step by step in the Maple programming language

Published on 12 May 2024 09:40 PM
#Maple

How to resolve the algorithm Kaprekar numbers step by step in the Maple programming language

Table of Contents

Problem Statement

A positive integer is a Kaprekar number if: Note that a split resulting in a part consisting purely of 0s is not valid, as 0 is not considered positive.

10000 (1002) splitting from left to right:

Generate and show all Kaprekar numbers less than 10,000.

Optionally, count (and report the count of) how many Kaprekar numbers are less than 1,000,000.

The concept of Kaprekar numbers is not limited to base 10 (i.e. decimal numbers); if you can, show that Kaprekar numbers exist in other bases too.

For this purpose, do the following:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Kaprekar numbers step by step in the Maple programming language

Source code in the maple programming language

isKaprekar := proc(n::posint) 
local holder, square, num_of_digits, k, left, right;
holder := true;
if n = 1 then 
 holder := true; 
else 
 holder := false; 
 square := n^2; 
 num_of_digits := length(n^2); 
 for k to num_of_digits do left := floor(square/10^k); 
     right := irem(square, 10^k); 
     if left + right = n and right <> 0 then 
        holder := true; 
     break; 
     end if; 
 end do; 
end if;
return holder; 
end proc;

showKaprekar := n -> select(isKaprekar, select(x -> irem(x, 9) = 1 or irem(x, 9) = 0, [seq(1 .. n - 1)]));

countKaprekar := n -> nops(showKaprekar(n));

showKaprekar(10000);
countKaprekar(1000000);

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