Kaprekar numbers: Difference between revisions

Line 1:

In this task, generate andshow all Kaprekar numbers less than 10,000. For extra credit, count (and report the count of) how many Kaprekar numbers are less than 1,000,000.

⚫

A positive integer is a [[wp:Kaprekar number|Kaprekar number]] if it is 1, or if the string representation of its square ~~can~~ be split once into parts consisting of positive integers that ~~when summed add up~~ to the original number.

⚫

A positive integer is a [[wp:Kaprekar number|Kaprekar number]] if it is 1, or if the string representation of its square may be split once into parts consisting of positive integers that sum to the original number.

⚫

~~For example~~ 2223 is a Kaprekar number as 2223*2223 == 4941729 and 494 + 1729 == 2223

;Example Kaprecar numbers:

⚫

The series of Kaprekar numbers begins: [[oeis:A006886|1, 9, 45, 55, ...]].

⚫

* 2223 is a Kaprekar number, as 2223*2223 = 4941729, 4941729 may be split to 494 and 1729, and 494 + 1729 = 2223

⚫

* The series of Kaprekar numbers begins: [[oeis:A006886|1, 9, 45, 55, ...]].

;Example process:

The task is to generate and show all the Kaprekar numbers less than 10,000

⚫

10000 (100<sup>2</sup>) splitting from left to right:

* The first split is [1, 0000], which is not OK because "a split of all zeroes is not counted; zero is not considered positive".

* Slight optimization opportunity: When splitting from left to right, once the right part consists of all zeroes, no further testing is needed; all further splits would also be invalid.

As a stretch goal count and show how many Kaprekar numbers there are that are less than one million.

;Reference:

Line 14:

Line 18:

;Note

In comparing splits of the square, a split of all zeroes is not counted ~~- as~~ zero is not considered positive.

In comparing splits of the square, a split of all zeroes is not counted; zero is not considered positive.

⚫

~~Example:~~ 10000 (100<sup>2</sup>) splitting from left to right:

The first split is [1, 0000], which is not OK because "a split of all zeroes is not counted - as zero is not considered positive". Slight optimization opportunity: When splitting from left to right, once the right part becomes all zeroes, you don't need to test this number anymore because its splits will always be invalid.

=={{header|C}}==