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Tom, Dick and Harry must die

Problem of the Three Prisoners

Tom, Dick, and Harry are awaiting execution while imprisoned in separate cells in some remote country.

The monarch of that country arbitrarily decides to pardon one of the three, but the name of the lucky man is not announced immediately, and the warden is forbidden to inform any of the prisoners of his fate.

Dick is alone with the warden. Dick argues that he already knows that at least Tom or Harry must be executed. Dick convinces the compassionate warden that by naming which one will die, either Tom or Harry, he will not be violating his instructions.

The warden names Harry.

Did this change the chances of Dick and Tom being freed?

It is not what you would think!