Difference between revisions of "1960 AHSME Problems/Problem 16"
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In the numeration system with base <math>5</math>, counting is as follows: <math>1, 2, 3, 4, 10, 11, 12, 13, 14, 20,\ldots</math>. | In the numeration system with base <math>5</math>, counting is as follows: <math>1, 2, 3, 4, 10, 11, 12, 13, 14, 20,\ldots</math>. |
Revision as of 00:04, 11 May 2018
Problem
In the numeration system with base , counting is as follows: . The number whose description in the decimal system is , when described in the base system, is a number with:
Solution
Since , divide by . The quotient is and the remainder is , so rewrite the number as Similarly, dividing by results in quotient of and remainder of , so rewrite the number as . Thus, the number in base can be written as , so the answer is
See Also
1960 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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All AHSME Problems and Solutions |