I think there is a simple approach to handling these problems. First define a number than no one knows anything about. Say BB(10) where BB is the busy beaver function. No one knows anything much about the size of this number, whether its odd or even, etc. Then if someone yes yes to:
BB(10), BB(10) + 2, BB(10) + 4 you can infer they probably really are using rule: n, n+2, n+4.
If its not this rule they may need to say they can’t tell if the sequence follows the rules or not.
Unless they are using very general and hard to guess rules this method seems effective. An example of an absurdly hard to guess rule would be. “All numbers are less than BB(100)”
This doesn’t solve the problem. If you think the rule is n,2n,3n you could try BB(10), 2BB(10), 3BB(10) but then the rule might really be: n,kn,(k+1)n for some k. But again this method seems to me like it would give you a way to check most “easy” rules. Or at least something like this is useful in testing your theories.
I think there is a simple approach to handling these problems. First define a number than no one knows anything about. Say BB(10) where BB is the busy beaver function. No one knows anything much about the size of this number, whether its odd or even, etc. Then if someone yes yes to:
BB(10), BB(10) + 2, BB(10) + 4 you can infer they probably really are using rule: n, n+2, n+4.
If its not this rule they may need to say they can’t tell if the sequence follows the rules or not.
Unless they are using very general and hard to guess rules this method seems effective. An example of an absurdly hard to guess rule would be. “All numbers are less than BB(100)”
This doesn’t solve the problem. If you think the rule is n,2n,3n you could try BB(10), 2BB(10), 3BB(10) but then the rule might really be: n,kn,(k+1)n for some k. But again this method seems to me like it would give you a way to check most “easy” rules. Or at least something like this is useful in testing your theories.