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.
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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!
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!----------------- 3.14159265358979323846264338327950288... Nothing Here
What's wrong with trying to test more numbers, see if you can discover any patterns? 11 follows the rule.----------------- 3.14159265358979323846264338327950288... Nothing Here
Hint: If a number follows the rule, then writing the number backwards will still satisfy the rule. So since 65536 works, so does 63556.----------------- 3.14159265358979323846264338327950288... Nothing Here
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.
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.
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.----------------- 3.14159265358979323846264338327950288... Nothing Here
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.
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.----------------- 3.14159265358979323846264338327950288... Nothing Here
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.
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.----------------- 3.14159265358979323846264338327950288... Nothing Here