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Mathematic Fun by Awoofawo(m): 11:32am On Oct 30, 2015 |
Steps to find the Kaprekar
Constant : 1) Choose any 3-digit number whose digits are not all the same. 2) Using these 3 digits, form the largest and smallest numbers possible. 3)Subract the smaller number from the larger number. 4) Take the result and repeat steps 2 and 3. to illustrate : ex. no.1 : 517 751 - 157 = 594 954 - 459 = 495 ex. no.2 : 397 973 - 379 = 594 954 - 459 = 495 ex. no.3 : 263 632 - 236 = 396 963 - 369 = 594 954 - 495 = 495 Note that each cycle ends at the number 495. 495 is called the Kaprekar Constant. |
Re: Mathematic Fun by Nobody: 12:53pm On Oct 30, 2015 |
Number: 211.
211-112 = 99
99-99 = 0 Number 212 221-122= 99 99-99=0 Number: 767 776 - 677= 99 99-99 =0 Other 3 digit numbers (60 in total) that don't converge to 495 are: 100, 101, 110, 111, 112, 121, 122, 211, 212, 221, 222, 223, 232, 233, 322, 323, 332, 333, 334, 343, 344, 433, 434, 443, 444, 445, 454, 455, 544, 545, 554, 555, 556, 565, 566, 655, 656, 665, 666, 667, 676, 677, 766, 767, 776, 777, 778, 787, 788, 877, 878 |
Re: Mathematic Fun by Awoofawo(m): 1:53pm On Oct 30, 2015 |
Karmanaut: The three digits must be different eg 345, 985 etc there a constant for four digits number too. Do you notice that you just discover something else? Let start with 325 re-arrange highest three digits number 532 and re-arrange to the smallest three digits number possible 235 do the maths the result is 495 |
Re: Mathematic Fun by Nobody: 8:47pm On Oct 31, 2015 |
Awoofawo:The rule was that all the numbers must not be the same, eg 111. there a constant for four digits number too.Yep. 6174. There's also one for 6 digit numbers: 549945, There's also one for 10 digit numbers: 9975084201. Do you notice that you just discover something else?Counter example: 656. 665 - 566 = 99 99 - 99 = 0 |
Re: Mathematic Fun by Awoofawo(m): 9:00pm On Oct 31, 2015 |
Karmanaut: In your last example, you can only have 6 or 9 once. No digit should appear twice! That is general rule to theorem! |
Re: Mathematic Fun by Nobody: 9:06pm On Oct 31, 2015 |
Awoofawo:Okay. |
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