A king has rounded up 1000 people suspected of counterfeiting coins, which look and feel the same as the official coin. However, only the official coin is truly fair (Pr(heads)=0.5), while all fake coins produce strongly skewed coin flip results (biased towards heads or tails).
The king decides to identify the counterfeiters by flipping a coin taken from each of the suspects. He leaves the actual flipping to 6 of his guards, handing them a suspected fake coin AND one official coin. The latter is to assure the king that his guards carried out the coin flips faithfully. Unfortunately, the king forgets to tell the guards how often to flip each coin, only that both coins (fake and official) must be flipped an equal number of times. All 1000 suspected fake coins tested in this manner go through the hands of all 6 guards.
Because heads of proven counterfeiters will roll, the king cannot afford to be wrong and commit too many innocent people to die. But he's comfortable executing up to 50 innocent people.
How should the king analyze the coin flip data from his 6 guards to identify the counterfeiters among the 1000 suspects? Can he also find a way to keep the number of innocently convicted under 50?
To get started, here's a sample from the first suspect (heads/tails):
Guard 1: suspect coin (88/11), official coin (42/47) Guard 2: suspect coin (38/5), official coin (22/21) Guard 3: suspect coin (115/15), official coin (70/60) Guard 4: suspect coin (39/33), official coin (35/37) Guard 5: suspect coin (70/13), official coin (43/40) Guard 6: suspect coin (22/18), official coin (19/21)