Problem:
A cryptographer devises the following method for encoding positive integers. First, the integer is expressed in base . Second, a -to- correspondence is established between the digits that appear in the expressions in base and the elements of the set . Using this correspondence, the cryptographer finds that three consecutive integers in increasing order are coded as , respectively. What is the base- expression for the integer coded as
Answer Choices:
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E.
Solution:
The fact that follows establishes and . Since follows immediately follows , and this establishes that . That follows also establishes that follows , so and . Hence .