Cross Purposes

A perplexing problem from the Pi Mu Epsilon Journal, Spring 1983:

In the little hamlet of Abacinia, the people use two base systems.

One resident says, “26 people use my base, base 10, and only 22 people speak base 14.”

Another says, “Of the 25 residents, 13 are bilingual and 1 is illiterate.”

All the residents speak the truth, but each (naturally) expresses numbers in her own base. How many residents are there?

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