Problem

The first expedition to Mars found only the ruins of a civilization. From the artifacts an...

The first expedition to Mars found only the ruins of a civilization. From the artifacts and pictures, the explorers deduced that the creatures who produced this civilization were four-legged beings with a tentacle that branched out at the end with a number of grasping “fingers.” After much study, the explorers were able to translate Martian mathematics. They found the following equation:

5x2 – 50x + 125 = 0

with the indicated solutions x = 5 and x = 8. The value x = 5 seemed legitimate enough, but x = 8 required some explanation. Then the explorers reflected on the way in which Earth’s number system developed, and found evidence that the Martian system had a similar history. How many fingers would you say the Martians had? (From The Bent of Tau Beta Pi, February 1956.)

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