The Kaprekar constant for a 4-digit number is 6174. To reach this constant, we apply a process known as Kaprekar’s routine:
Arrange the digits of the number in descending order.
Arrange the digits in ascending order.
Subtract the smaller number from the larger one.
Repeat the process until the result is 6174.
Let’s apply this to 5683 and see how many rounds it takes to reach the Kaprekar constant.
First round:
The largest number from digits 5683: 8653
The smallest number from digits 5683: 3568
Subtraction: 8653 – 3568 = 5085
Second round:
Largest number from digits of 5085: 8550
The smallest number from digits 5085: 0558 (which is 558 when leading zeros are omitted)
Subtraction: 8550 – 0558 = 7992
Third round:
The largest number from digits 7992: 9972
The smallest number from digits 7992: 2799
Subtraction: 9972 – 2799 = 7173
Fourth round:
The largest number from digits 7173: 7731
The smallest number from digits 7173: 1377
Subtraction: 7731 – 1377 = 6354
Fifth round:
The largest number from digits 6354: 6543
The smallest number from digits 6354: 3456
Subtraction: 6543 – 3456 = 3087
Sixth round:
The largest number from digits 3087: 8730
The smallest number from digits 3087: 0378 (or 378)
Subtraction: 8730 – 0378 = 8352
Seventh round:
The largest number from digits 8352: 8532
The smallest number from digits 8352: 2358
Subtraction: 8532 – 2358 = 6174
Conclusion:
It takes 7 rounds for the number 5683 to reach the Kaprekar constant 6174.
InText Questions (Page 66)