Quote:
Originally Posted by jbjb
Spoiler:
You can be certain of going free.
Pick 21 coins at random (you have no choice, assuming they are randomly positioned by the gaoler), and turn each one over before positioning it on your table. You will end up with the same number of Queen's heads as your gaoler.
Reasoning:
At the start, the gaoler has 21 more heads than you (he has 21 and you have none, as you have no coins).
Each time you pick a coin either it was a head on his table or not.
If it was a head on his table, you've turned it over to a coat of arms on your table - you've reduced his number of heads by one and made no difference to your number of heads.
If it was a coat of arms on his table, you've turned it over to a head on your table - increasing your count of heads by one and making no difference to his count.
I.e. each coin you move in this way will reduce the excess number of heads he has over you by one, irrespective of what the coin initially showed.
So, after you've moved 'n' coins this way, he will have '21-n' heads more than you. Once you've moved your chosen 21 coins, you and he will have the same number of heads. Hence, he won't have more heads than you and you therefore you go free
/JB |
Exactly right. Well done.