This game is based off of previous Guess the Secret Function threads found here, here, and here and some rules may be mercilessly stolen.
1. I, the referee, have a secret (not too complex) function f which is defined over all positive integers. This function is monotonically increasing.
2. To post a valid entry, post a number inside a spoiler which is bigger than your previous valid entry.
3. Each valid entry represents you hitting a golf ball towards a hole.
4. For each number you post, the referee (me) calculates the largest f(n) which isn't yet larger than that number. The n for which this is true, is called "the position of the posted number".
Say you post 413. I know that f(37)=407 and f(38)=416 so the position of your entry is 37 - the largest n for which f(n)<413.
5. Like in golf, your goal is to hit par resulting in a score of 0 (or less for beating par).
6. Your objective is to post a number which increments the position of your previous entry by 20
If on your first post, you guess a number at position 20, you get a hole in one.
If your fourth post was 413, which I announced to be at position 37, your goal, is to try and guess a number which will be at position 57. That is, you want to post a number which is between f(57) and f(58). Guessing correctly will result in scoring par.
7. Starting on your fifth guess, you are considered to be “on the green”. I’d recommend using your putter. Now to get your ball in the hole, all following attempted guesses only need be a number which increments your fourth guess by 20.
7b. While on the green, if you post a number that increments the positions of your by more than 20, (20+x) then you need only increase the position by x. Example:
Let’s say your objective is to post a number with a position of 57, but you end up at the position 60. To score, you need to increase the position by 3, so 63.
8. At any time if the increment N is more than 30, it is considered out of bounds and that guess counts as 2 hits.
Let’s say the secret function is f(n)=n^3+n^2+n
Your first guess is 1, which is at position 3. To get a hole in 2, you must find position 23.
Your second guess in 3, which is at position 39. Oh No! You increased your position by more than 30, so your ball goes out of bounds and also counts for your third guess.
Your fourth guess is 3.2, which is at position 46. Your final hole is currently found at position 66. You are now on the green.
Your fifth guess is 3.5, which is at position 58. Your final hole is still at position 66.
Your sixth guess is 3.7, which is at position 68. You passed your hole by an increment of 2, so your final hole is currently found at position 70.
Your seventh guess is 3.75, which is at position 70. Hole is 7, which is 2 above par (double bogie), so you scored 2 on this hole!
For all your silly time-killing forum games.
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