Kaprekars Constant
Kaprekar's constant
The number 6174 is known as Kaprekar's constant[| Kaprekar's Constant 6174] after the Indian mathematician D. R. Kaprekar. This number is renowned for the following rule:
Take any four-digit number, using at least two different digits (leading zeros are allowed). Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary. Subtract the smaller number from the bigger number. Go back to step 2 and repeat.
Video: https://www.youtube.com/watch?v=xtyNuOikdE4
z^3 Solution
1001..1010@kc;
function kc(x)
{
k=x.⁋.⪡.⋰;
kp:=k.⋱.⚯*1 -k.⋰.⚯;
_y=k;
var r=-1, rt=-1,rs=[];
(1..8)@(
function(i)
{
var t=kp(_y)
if(t==6174 && r==-1)
{
r=i;rt=t;rs.push(t);
throw("EXIT")
}
else
{
rs.push(t)
}
_y=t.⁋.⪡;
}
);
☝;
return([x,r,rs])
}
| x | kc | |||||||||
| 1001 |
| |||||||||
| 1002 |
| |||||||||
| 1003 |
| |||||||||
| 1004 |
| |||||||||
| 1005 |
| |||||||||
| 1006 |
| |||||||||
| 1007 |
| |||||||||
| 1008 |
| |||||||||
| 1009 |
| |||||||||
| 1010 |
|
Notes
In Loops (such as 1..7),
throw("EXIT")
or
throw("BREAK")
will break the FOR loop.
throw("CONTINUE")
will continue the FOR loop call.
In the code above, the throw("EXIT") is used to go break the loop as the loop has reached 6174 potentially.
Also note the elegant way to handle exceptions. For example, tryx or ☝; is a quick way to wrap the previous block or statement with a try{}catch(){} statement.