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=[];	
	try
	{
		(1..7)@(
			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.⁋.⪪;
			}
		);
	}
	catch(err)
	{
	}
	⊫([x,r,rt,rs])
	return([x,r,_y,rs])

}

Answer:

1001 4 6174 1089 9621 8352 6174 6174 6174 6174

1002 3 6174 2088 8532 6174 6174 6174 6174 6174

1003 3 6174 3087 8352 6174 6174 6174 6174 6174

1004 7 6174 4086 8172 7443 3996 6264 4176 6174

1005 7 6174 5085 7992 7173 6354 3087 8352 6174

1006 7 6174 6084 8172 7443 3996 6264 4176 6174

1007 3 6174 7083 8352 6174 6174 6174 6174 6174

1008 3 6174 8082 8532 6174 6174 6174 6174 6174

1009 4 6174 9081 9621 8352 6174 6174 6174 6174

1010 4 6174 1089 9621 8352 6174 6174 6174 6174

x	kc
1001	1001 4 6 1 7 4 1089 9621 8352 6174 6174 6174 6174
1002	1002 3 6 1 7 4 2088 8532 6174 6174 6174 6174 6174
1003	1003 3 6 1 7 4 3087 8352 6174 6174 6174 6174 6174
1004	1004 7 4 1 7 6 4086 8172 7443 3996 6264 4176 6174
1005	1005 7 8 3 5 2 5085 7992 7173 6354 3087 8352 6174
1006	1006 7 4 1 7 6 6084 8172 7443 3996 6264 4176 6174
1007	1007 3 6 1 7 4 7083 8352 6174 6174 6174 6174 6174
1008	1008 3 6 1 7 4 8082 8532 6174 6174 6174 6174 6174
1009	1009 4 6 1 7 4 9081 9621 8352 6174 6174 6174 6174
1010	1010 4 6 1 7 4 1089 9621 8352 6174 6174 6174 6174