A machine holds a hidden whole number, and a rule is secretly changing it.

You have some prior knowledge: the true rule is always one of a small set of possibilities. You'll see that set when you begin.

You never see the actual current number — only whether it is even or odd. Even shows as 0, odd shows as 1.

Each round, you run an experiment: feed the machine a digit from 0 to 9. The hidden rule combines it with the secret number, and you see whether the result is now even or odd.

That stream of evens and odds, and your past experiments, is all you have. From both, work out which rule is at work.

When you're ready, publish: name the rule you've identified — or declare the rules cannot be told apart.

Your paper is accepted only if the evidence bears it out.