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This IQ Test Logic Problem is Challenging

This logic problem comes to us all the way from the 1930's, but was known in other versions long before that. Can you shed some light on the solution? Remember, you'll only have one guess so use it wisely! Think well of the question, and any pitfalls it might have, and then select the answer you believe to be correct. Don't worry, the whole thing will be explained to you if you don't get it right!

 
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