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diff --git a/daily/287easy/README.md b/daily/287easy/README.md new file mode 100644 index 0000000..2ef0423 --- /dev/null +++ b/daily/287easy/README.md @@ -0,0 +1,64 @@ +# [[2016-10-10] Challenge #287 [Easy] Kaprekar's Routine](https://www.reddit.com/r/dailyprogrammer/comments/56tbds/20161010_challenge_287_easy_kaprekars_routine/) + +## Description + +Write a function that, given a 4-digit number, returns the largest digit in +that number. Numbers between 0 and 999 are counted as 4-digit numbers with +leading 0's. + + largest_digit(1234) -> 4 + largest_digit(3253) -> 5 + largest_digit(9800) -> 9 + largest_digit(3333) -> 3 + largest_digit(120) -> 2 + +In the last example, given an input of `120`, we treat it as the 4-digit number +`0120`. + +*Today's challenge is really more of a warmup for the bonuses. If you were able +to complete it, I highly recommend giving the bonuses a shot!* + +## Bonus 1 + +Write a function that, given a 4-digit number, performs the "descending digits" +operation. This operation returns a number with the same 4 digits sorted in +descending order. + + desc_digits(1234) -> 4321 + desc_digits(3253) -> 5332 + desc_digits(9800) -> 9800 + desc_digits(3333) -> 3333 + desc_digits(120) -> 2100 + +## Bonus 2 + +Write a function that counts the number of iterations in Kaprekar's Routine, +which is as follows. + +Given a 4-digit number *that has at least two different digits*, take that +number's descending digits, and subtract that number's ascending digits. For +example, given `6589`, you should take `9865 - 5689`, which is `4176`. Repeat +this process with `4176` and you'll get `7641 - 1467`, which is `6174`. + +Once you get to 6174 you'll stay there if you repeat the process. In this case +we applied the process 2 times before reaching 6174, so our output for `6589` +is `2`. + + kaprekar(6589) -> 2 + kaprekar(5455) -> 5 + kaprekar(6174) -> 0 + +Numbers like 3333 would immediately go to 0 under this routine, but since we +require at least two different digits in the input, all numbers will eventually +reach 6174, which is known as Kaprekar's Constant. Watch +[this video](https://www.youtube.com/watch?v=d8TRcZklX_Q) if you're still +unclear on how Kaprekar's Routine works. + +What is the largest number of iterations for Kaprekar's Routine to reach 6174? +That is, what's the largest possible output for your `kaprekar` function, given +a valid input? Post the answer along with your solution. + +*Thanks to [/u/BinaryLinux](https://www.reddit.com/u/BinaryLinux) and +[/u/Racoonie](https://www.reddit.com/u/Racoonie) for posting the idea behind +this challenge in +[/r/daliyprogrammer_ideas](https://www.reddit.com/r/daliyprogrammer_ideas)!* |