1987 AHSME Problems/Problem 16
Problem
A cryptographer devises the following method for encoding positive integers. First, the integer is expressed in base . Second, a 1-to-1 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 ?
Solution
Since , i.e. adding causes the "fives" digit to change, we must have and . Now since , we have . Finally, note that in , adding will cause the "fives" digit to change by if it changes at all, so , and thus since and are the only digits left (we already know which letters are assigned to , , and ), we must have and . Thus , which is answer .
See also
1987 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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