Alright, here’s how the game works:
There is a rule-maker, and everyone else tries to guess the rule.
The rule-maker creates a rule mentally, that governs a set of 3 numbers.
He then provides an example of a set of 3-or-4 numbers that follows the rule.
Everyone else then gives various 3-or-4 number sets as experiments, to see if they follow the rule, and the Rule Maker has to indicate whether any given set is correct.
The number of experiments the guessers are allowed to make is unlimited.
There are some meta-rules, of course, governing what the rules can be –
The rules have to allow for an infinite amount of positive and negative results.
In other words, if your rule is such that there is only 1 correct sequence, nothing that happened while you were the rule-maker counts.
And furthermore, we will find you and tattoo something horrible onto your forehead, because nobody likes people who spoil games like that.
The rule has to be something that is feasibly guessable.
I can’t think of any counter-examples at the moment, but if you think of one that is just too crazy to be guessed in a reasonable time…the game is only fun if you can win eventually, and the point is for this to be enjoyable for the people involved.
If there are multiple rule sets that would produce the same output of ‘positive’ and ‘negative’ results, and someone gives one that produces the same results as the rule you thought of but they worded it differently, they get a point for it.
In other words, if your rule is that all 3 numbers have to be even, and someone’s guess is that all numbers have to be divisible by 2, or are the result of taking an odd number and adding 1, or some other variant that would produce an equivalent set, then they get the point, and if you as the rule-maker say that they were wrong, and it’s later demonstrable that they were right, you lose a point.
Adding this for extra clarity: the rules have to be fully functionally equivalent. Not just for the tests that have already been performed, but for all tests. It’s easy to see why ‘even’ and ‘divisible by 2’ are fully functionally equivalent, not just for a finite set of tests but for all conceivable tests.
The sets have to be integers
You may use decimals in your rules somehow, provided they follow rule2 above – being feasibly guessable – but the output has to be integers. If that means that your algorithm for an output involves rounding somehow, do that.
If you’ve been the rule-maker for a week and nobody’s guessed correctly, you must relinquish your seat to whoever is the first to notice it’s been a week (a week since the prior rulemaker announced that you were correct) and give the correct answer. If the rule is seen to be unguessable by enough people, you lose 3 points (that way there’s a penalty for making a rule too complicated). If at any point you mistakenly told people that a certain set was not following the rule and it was, or vice versa, you lose 2 points.
Now, here’s how to make things interesting:
If you guess right, you get +2 point.
If you guess wrong, you get -1 points.
Guesses are not free – if you’re wrong, you pay.
So, experiment, ask the Rule Maker as many examples as you can. Prior to guessing. Experiments are free, guesses are not.
Whoever guesses right is the next rule maker.
I’m just going to show an example of how it might go: