Kaprekar's constant
The number 6174 is known as Kaprekar's constant[1][2][3] 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⁋)#).sort();
kp:=((k⋱)⚯*1 -(k⋰)⚯);
_y=k;
var r=-1;
var rt=-1;
var 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⁋)#);
//⊫("AFTER",i,_y);
}
);
}
catch(err)
{
}
⊫([x,r,rt,rs])
return([x,r,_y,rs])
}
{| style="" id="TABLE1" class="null wikitable" donotcaption="true" |
|-
| style="cursor: auto;" |
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1001
|-
| style="cursor: auto;" | 4
|-
| 6174
|-
| 1089
| 9621
| 8352
| 6174
| 6174
| 6174
| 6174
|}
|}
{| style="" id="TABLE1" class="null wikitable" donotcaption="true" |
|-
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1002
|-
| 3
|-
| 6174
|-
| 2088
| 8532
| 6174
| 6174
| 6174
| 6174
| 6174
|}
|}
{| style="" id="TABLE1" class="null wikitable" donotcaption="true" |
|-
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1003
|-
| 3
|-
| 6174
|-
| 3087
| 8352
| 6174
| 6174
| 6174
| 6174
| 6174
|}
|}
{| style="" id="TABLE1" class="null wikitable" donotcaption="true" |
|-
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1004
|-
| 7
|-
| 6174
|-
| 4086
| 8172
| 7443
| 3996
| 6264
| 4176
| 6174
|}
|}
{| style="" id="TABLE1" class="null wikitable" donotcaption="true" |
|-
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1005
|-
| 7
|-
| 6174
|-
| 5085
| 7992
| 7173
| 6354
| 3087
| 8352
| 6174
|}
|}
{| style="" id="TABLE1" class="null wikitable" donotcaption="true" |
|-
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1006
|-
| 7
|-
| 6174
|-
| 6084
| 8172
| 7443
| 3996
| 6264
| 4176
| 6174
|}
|}
{| style="" id="TABLE1" class="null wikitable" donotcaption="true" |
|-
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1007
|-
| 3
|-
| 6174
|-
| 7083
| 8352
| 6174
| 6174
| 6174
| 6174
| 6174
|}
|}
{| style="" id="TABLE1" class="null wikitable" donotcaption="true" |
|-
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1008
|-
| 3
|-
| 6174
|-
| 8082
| 8532
| 6174
| 6174
| 6174
| 6174
| 6174
|}
|}
{| style="" id="TABLE1" class="null wikitable" donotcaption="true" |
|-
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1009
|-
| 4
|-
| 6174
|-
| 9081
| 9621
| 8352
| 6174
| 6174
| 6174
| 6174
|}
|}
{| style="" id="TABLE1" class="null wikitable" donotcaption="true" |
|-
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1010
|-
| 4
|-
| 6174
|-
| 1089
| 9621
| 8352
| 6174
| 6174
| 6174
| 6174
|}
|}
{| style="" id="TABLE1" class="null withtitle wikitable" donotcaption="true" |
|-
| x
| kc
|-
| 1001
| style="cursor: col-resize;" |
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1001
|-
| 4
|-
| 6
| 1
| 7
| 4
|-
| 1089
| 9621
| 8352
| 6174
| 6174
| 6174
| 6174
|}
|-
| 1002
| style="cursor: col-resize;" |
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1002
|-
| 3
|-
| 6
| 1
| 7
| 4
|-
| 2088
| 8532
| 6174
| 6174
| 6174
| 6174
| 6174
|}
|-
| 1003
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1003
|-
| 3
|-
| 6
| 1
| 7
| 4
|-
| 3087
| 8352
| 6174
| 6174
| 6174
| 6174
| 6174
|}
|-
| 1004
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1004
|-
| 7
|-
| 4
| 1
| 7
| 6
|-
| 4086
| 8172
| 7443
| 3996
| 6264
| 4176
| 6174
|}
|-
| 1005
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1005
|-
| 7
|-
| 8
| 3
| 5
| 2
|-
| 5085
| 7992
| 7173
| 6354
| 3087
| 8352
| 6174
|}
|-
| 1006
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1006
|-
| 7
|-
| 4
| 1
| 7
| 6
|-
| 6084
| 8172
| 7443
| 3996
| 6264
| 4176
| 6174
|}
|-
| 1007
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1007
|-
| 3
|-
| 6
| 1
| 7
| 4
|-
| 7083
| 8352
| 6174
| 6174
| 6174
| 6174
| 6174
|}
|-
| 1008
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1008
|-
| 3
|-
| 6
| 1
| 7
| 4
|-
| 8082
| 8532
| 6174
| 6174
| 6174
| 6174
| 6174
|}
|-
| 1009
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1009
|-
| 4
|-
| 6
| 1
| 7
| 4
|-
| 9081
| 9621
| 8352
| 6174
| 6174
| 6174
| 6174
|}
|-
| 1010
|
{| style="" id="TABLE1" class="notepad" donotcaption="true" |
|-
| 1010
|-
| 4
|-
| 6
| 1
| 7
| 4
|-
| 1089
| 9621
| 8352
| 6174
| 6174
| 6174
| 6174
|}
|}