Difference between revisions of "Kaprekars Constant"

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(Created page with " =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:...")
 
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| 1001
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| style="cursor: auto;" | 4
 +
 +
|-
 +
| 6174
 +
 +
|-
 +
| 1089
 +
| 9621
 +
| 8352
 +
| 6174
 +
| 6174
 +
| 6174
 +
| 6174
 +
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|}
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{| style="" id="TABLE1" class="null wikitable" donotcaption="true" |
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{| style="" id="TABLE1" class="notepad" donotcaption="true" |
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|-
 +
| 1002
 +
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|-
 +
| 3
 +
 +
|-
 +
| 6174
 +
 +
|-
 +
| 2088
 +
| 8532
 +
| 6174
 +
| 6174
 +
| 6174
 +
| 6174
 +
| 6174
 +
 +
 +
|}
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|}
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{| style="" id="TABLE1" class="null wikitable" donotcaption="true" |
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|
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{| style="" id="TABLE1" class="notepad" donotcaption="true" |
 +
|-
 +
| 1003
 +
 +
|-
 +
| 3
 +
 +
|-
 +
| 6174
 +
 +
|-
 +
| 3087
 +
| 8352
 +
| 6174
 +
| 6174
 +
| 6174
 +
| 6174
 +
| 6174
 +
 +
 +
|}
 +
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 +
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|}
 +
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{| 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
 +
 +
 +
|}
 +
 +
 +
 +
|}
 
</pre>
 
</pre>

Revision as of 22:28, 1 September 2024

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


|}



|}
Retrieved from "http://wiki.zcubes.com/index.php?title=Kaprekars_Constant&oldid=217362"