Difference between revisions of "1960 AHSME Problems/Problem 16"
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− | == Problem | + | == Problem == |
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 |