Go to the bank. Obtain several thousand coins of a denomination equal to the one you are looking for.
This was the first approach I thought of. Make a haystack for the needle.
This will however allow you to find the haystack.
"Where is the coin? Right here, in the pile of coins."
Your coin finding self could beat your coin hiding self by scooping up all the coins,
bringing them before a judge and arbiter and saying "here it is."
You will likely have found the coin, even if you can not identify it.
If a judge can easily identify the coin, and you have found and presented the coin to the judge,
then it would be reasonable to say the coin is found.
Otherwise, the answer is lost to both the judge and the coin hider, much as if you ground it to a fine dust.
Save yourself the trouble and grind the coin into dust.
Destroy the answer. Make retrieval impossible.
(This was probably intended to be forbidden in the formulation of the problem, but it is not.)
Your coin finding self could beat your coin hiding self by scooping up all the coins, bringing them before a judge and arbiter and saying "here it is."
In that case, lock away the coin and hide the key among thousands of identical keys. Surely a wheelbarrow full of keys would not constitute a coin.
And if identifying the locked chamber (or container, or whatever) counts as finding the coin, then lock a bunch of them after hiding the coin in a randomly selected one.
I formulated a little problem. Care to solve it?
You are given the following information:
Your task is to hide a coin in your house (or any familiar finite environment).
After you've hidden the coin your memory will be erased and restored to a state just before you receiving this information.
Then you will be told about the task (i.e that you have hidden a coin), and asked to try to find the coin.
If you find it you'll lose, but you will be convinced that if you find it you win.
So now you're faced with finding an optimal strategy to minimize the probability of finding the coin within a finite time-frame.
Bear in mind that any chain of reasoning leading up to a decision of location can be generated by you while trying to find the coin.
You might come to the conclusion that there cant exist an optimal strategy other than randomizing. But if you randomize, then you have the risk of placing the coin at a location where it can be easily found, like on a table or on the floor. You could eliminate those risky locations by excluding them as alternatives in your randomization process, but that would mean including a chain of reasoning!