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      CommentAuthorMathdude314 (Advanced Member)
    • CommentTimeMay 8th 2016 edited
     
    OK, so I absolutely failed last time I tried to host a Find the Rule game. It's exactly the same game. I have a secret rule which certain whole numbers follow and certain ones do not. You have to find that rule.

    A vastly superior alien race wants to take over Earth. However they are not allowed to destroy planets with highly intelligent life forms. So they have decided to run a test. They randomly beam people (either one at a time or in groups) to their ship, and pose a puzzle.

    The puzzle always goes something like this: there is a secret rule that certain whole numbers follow and others do not follow. You try to figure out the pattern by guessing numbers, and you will be told if they follow the rule or not. Your goal is to guess the secret rule. If you aren\\'t correct, the aliens will provide a counterexample to disprove it.


    So what I'm going to do is start you off with three of each type (three yes numbers and three no numbers). After that, you can test as many numbers as you like, although I'm not a fan of brute force searches on this game, so I introduce the...

    TEST LIMIT
    You are limited to 5 pending tests per user, which means that you can test up to 5 numbers, wait for me to answer, and then test up to 5 more, etc.

    Also when you try to take a guess at the secret rule, please either whisper or use a spoiler. This way, guests who read the forums can take a crack at it.

    ——————————————

    TLDR: Find the pattern between the "yes" and "no" numbers. You can test up to 5 numbers at once and then try to guess the rule.


    This is the one we are currently solving.
    Yes: all single-digit numbers, 11, 22, 33, 44, 55, 63 556, 65 536, 2 097 152
    No: 10, 14, 20, 455, 243, 3377, 7734
    Hints:
    1. If you write the number backwards, the result is the same.
    2. The order of the digits is important.
    3. A number with all digits different will never satisfy the rule — UNLESS it\'s a single digit number, which always DOES work.
    4. The fact that leading zeroes are not allowed has a real effect. Yes, there are some numbers which, when written with leading zeros, change from a yes to a no, or vice versa!



    These puzzles will not be updated again.

    Follow: 21439, 145, 12321, 556677
    Break: 314, 927532, 7, 6543, 3344
    The order of the digits matters.

    For a three-digit number, all digits must be different. But 314 is a no.

    The rule involves three of the number\\\'s digits. As such, one- and two-digit numbers break the rule by default.

    Yes: 56789, 2145, 40708
    No: 321, 664422, 901

    There must be three digits in strict ascending order from left to right. (They don\\\'t have to be next to each other!!)



    -----------------
    If less people are active, that will only make for even less activity. Start making those designs!
    Currently working on a one-round no-elimination quick RP game...
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      CommentAuthorMathdude314 (Advanced Member)
    • CommentTimeMay 8th 2016 edited
     
    PUZZLE 1

    I'm going to start with an easy one. I have an interesting puzzle but it might be too hard.
    The space is a thousands separator since the comma is used to separate the numbers.

    Yes: all single-digit numbers, 11, 22, 33, 44, 55, 63 556, 65 536, 2 097 152
    No: 10, 14, 20, 455, 243, 3377, 7734
    Hints:
    1. If you write the number backwards, the result is the same.
    2. The order of the digits is important.
    3. A number with all digits different will never satisfy the rule — UNLESS it's a single digit number, which always DOES work.
    4. The fact that leading zeroes are not allowed has a real effect. Yes, there are some numbers which, when written with leading zeros, change from a yes to a no, or vice versa!-----------------
    If less people are active, that will only make for even less activity. Start making those designs!
    Currently working on a one-round no-elimination quick RP game...
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      CommentAuthorTapir
    • CommentTimeMay 10th 2016
     
    Looks all think this one is too easy, so, next pls. :)-----------------
    My games: Tapir Games
    My phyards: Tapir@phyard
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      CommentAuthorBioManiac R2 (Moderator)
    • CommentTimeMay 10th 2016
     
    "easy one" "might be too hard"

    is too hard for me to want to spend time figuring it out lol sorry
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      CommentAuthorMathdude314 (Advanced Member)
    • CommentTimeMay 10th 2016
     
    What's wrong with trying to test more numbers, see if you can discover any patterns? 11 follows the rule.-----------------
    If less people are active, that will only make for even less activity. Start making those designs!
    Currently working on a one-round no-elimination quick RP game...
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      CommentAuthorBioManiac R2 (Moderator)
    • CommentTimeMay 12th 2016
     
    1, 2, 3, 5, 6, 7, 8, 9, 10
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      CommentAuthorMathdude314 (Advanced Member)
    • CommentTimeMay 12th 2016
     
    All of them except 10 follow the rule.-----------------
    If less people are active, that will only make for even less activity. Start making those designs!
    Currently working on a one-round no-elimination quick RP game...
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      CommentAuthorBioManiac R2 (Moderator)
    • CommentTimeMay 12th 2016
     
    i still have no idea.
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      CommentAuthorMathdude314 (Advanced Member)
    • CommentTimeMay 13th 2016
     
    33 follows the rule. Look closely at the digits.

    Hint: If a number follows the rule, then writing the number backwards will still satisfy the rule. So since 65536 works, so does 63556.-----------------
    If less people are active, that will only make for even less activity. Start making those designs!
    Currently working on a one-round no-elimination quick RP game...
    • CommentAuthorXyuzhg (Moderator)
    • CommentTimeMay 13th 2016
     
    If I'm not mistaken:

    Let f(n) denote the number of cases following the rule in {0, 1, 2, ..., n}. Then if k is a positive integer, f(10k) = 9 + k.-----------------
    Hopefully PA is inconsistent.
    • CommentAuthorpuzzle geek (Advanced Member)
    • CommentTimeMay 13th 2016
     
    so, Is K the number guessed? or is 10K the number guessed meaning that for stuff like 4, K would be 0.4?

    if K is the guessed number, then for 33, 330 =? 9 + 33 which is false... in case two 10(3.3) = 9 + 3.3 which also isn't true... uhh....

    So, im guessing 14 and 20 do NOT follow the pattern.
    I think it has something to do with the sum of all the digits in the number

    Oh btw, I never left the forum :P
    I'm just lurking mostly now.-----------------
    puzzled
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      CommentAuthorMathdude314 (Advanced Member)
    • CommentTimeMay 13th 2016
     
    I think you are mistaken, Xyuzhg. 14 and 20 are fail numbers, will add to the list.

    I decided to add another hint.-----------------
    If less people are active, that will only make for even less activity. Start making those designs!
    Currently working on a one-round no-elimination quick RP game...
    • CommentAuthorpuzzle geek (Advanced Member)
    • CommentTimeMay 14th 2016
     
    ok, how I got 14 and 20: I added to of the earlier fail numbers together and those were the results.

    Im wondering now about 22 44 and 55. I think 22 and 44 will work, but 55 will not.-----------------
    puzzled
    • CommentAuthorXyuzhg (Moderator)
    • CommentTimeMay 14th 2016
     
    puzzle geek, k = 3.3 is not a positive integer. The expression gives you only the case when n, the largest guess, is a multiple of 10. You should read carefully what I wrote, and possibly learn what a function does.

    Mathdude314, can you evaluate the actual values of f(100) and f(1000)? Nothing so far contradicts my guess, and I've also taken the liberty to empirically verify my formula.-----------------
    Hopefully PA is inconsistent.
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      CommentAuthorMathdude314 (Advanced Member)
    • CommentTimeMay 15th 2016 edited
     
    puzzle geek, they (22,44,55) all work.
    Xyuzhg, Perhaps you were right. I can't prove the formula, but I can't disprove it.-----------------
    If less people are active, that will only make for even less activity. Start making those designs!
    Currently working on a one-round no-elimination quick RP game...
    • CommentAuthorXyuzhg (Moderator)
    • CommentTimeMay 15th 2016
     
    You can prove the formula easily by induction. The base case holds from the information given in the thread, and the inductive step is simple from just looking at how many cases can hold between each multiple of 10.-----------------
    Hopefully PA is inconsistent.
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      CommentAuthorMathdude314 (Advanced Member)
    • CommentTimeMay 19th 2016
     
    I added yet another hint, because Xyuzhg obviously solved it and nobody else posted anything. (I said to whisper guesses, but I haven't received even one whisper.)
    There will be a more interesting puzzle next.-----------------
    If less people are active, that will only make for even less activity. Start making those designs!
    Currently working on a one-round no-elimination quick RP game...
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      CommentAuthorBioManiac R2 (Moderator)
    • CommentTimeMay 19th 2016
     
    I looked at the answer and it tells me that half the numbers and hints you gave made no sense...

    according to you answer, no single or double digits should work, also the hint "writing the number backwards will always work" doesn't make sense, since 123 works but 321 does not.
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      CommentAuthorMathdude314 (Advanced Member)
    • CommentTimeMay 19th 2016
     
    You peeked at the ARCHIVES, which has puzzles from the past. (It's the one about ascending order, right?)
    The current puzzle is the one we're discussing in this thread.

    I want to make a VERY important clarification for this puzzle, which could change the status of certain numbers: Leading Zeros are NOT ALLOWED.-----------------
    If less people are active, that will only make for even less activity. Start making those designs!
    Currently working on a one-round no-elimination quick RP game...
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      CommentAuthorBioManiac R2 (Moderator)
    • CommentTimeMay 20th 2016
     
    #sadly still has no interest to solve the puzzle :/
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      CommentAuthorMathdude314 (Advanced Member)
    • CommentTimeMay 20th 2016
     
    Would you like me to give the answer away and try a more interesting one?-----------------
    If less people are active, that will only make for even less activity. Start making those designs!
    Currently working on a one-round no-elimination quick RP game...
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      CommentAuthorBioManiac R2 (Moderator)
    • CommentTimeMay 21st 2016
     
    #zzzz idk.... i'm not interested in these puzzles... I like my CI stuff... that's why I come check here