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This is a simple game based on the "2-4-6 task" coined by Peter Wason; if you're familiar with it, you mostly know how to play. The rules are as follows :
- I am the cruel and arbitrary warden of a prison, and you are my prisoner.
- I'm thinking of a rule which is expressed as a natural language sentence in English of 40 words or less. The goal of the game is to guess what my rule is. Do so three times, and win your freedom.
- My rule describes some kind of relationship between triplets of integers between 0 and 999, inclusive.
- You can only take two actions : either test a triplet, or try to guess the rule.
- To test a triplet, just post any three integers according to the constraints described above. I will tell you whether they follow my rule.
- You can test as many triplets as you want. You can test one triplet per post.
- If you think you know the rule, you can try to guess it at any time. But he careful : For each wrong guess, you lose one Mercy. You have ten Mercies. Lose them all, and lose your chance at freedom, forever.
- For each rule you guess right, I will return two Mercies to you, and I will choose a new rule. Guess three rules correctly before you lose all your Mercies, and freedom is yours.
- You don't have to guess the exact wording. For example, the rule "all three numbers must be coprime" is equivalent to "none of the three numbers may have any common divisors besides 1". Two rules are equivalent if, for all possible sets of integers, any set that fails one rule fails the other, and any set that follows one rule follows the other.
- For our game, zero is even, and 2 is the smallest prime.
- As a gift, I will allow you a clue when you guess an incorrect rule. I will show you a triplet which follows one rule and fails the other. I won't tell you whether it's my rule it follows or your guessed rule.
- When my rule is guessed, you can go back and check for yourself that my answers match correctly. Thus, you know I must be honest, and don't need to trust me; if I cheat, you will know.
- When writing a rule, instead of "the first number" etc., you can use letters to refer to arbitrary integers in a triplet (A, B, C).
- Secretly, I want you to win.
The game begins.
This triplet follows my rule : ( 3, 6, 7 )
What will you test first?
