Hey today i was surfing the net and guess what i found something new and interesting…
Here it is…Check It out
6174 is known as Kaprekar’s constant after the Indian mathematician D. R. Kaprekar. This number is notable for the following property:
1. Take any four-digit number with at least two digits different. (Leading zeros are allowed.)2. Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary.3. Subtract the smaller number from the bigger number.4. Go back to step 2.
The above operation, known as Kaprekar’s operation, will always reach 6174 in at most 7 steps and it stops there. Once 6174 is reached, the process will keep yielding 7641 – 1467 = 6174. For example, choose 3524:
5432 – 2345 = 30878730 – 0378 = 83528532 – 2358 = 6174
The only four-digit numbers for which this function does not work are repdigits such as 1111, which give the answer 0 after a single iteration. All other four-digits numbers work if leading zeros are used to keep the number of digits at 4:
2111 – 1112 = 09999990 – 0999 = 8991 (rather than 999 – 999 = 0)9981 – 1899 = 80828820 – 0288 = 85328532 – 2358 = 6174
495 has the same property for three-digit numbers. For five-digit numbers and above, the function does not settle down to a single value, but instead cycles through one of several series of values.
Cool Naa
source — wiki
Subscribe to:
Post Comments (Atom)

No comments:
Post a Comment