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Suppose that $n$ is a positive integer such that in base $7$, then $n$ can be expressed as $\overline{ABC}_7$, and in base $11$...Asked by Charles
I need help fast
Suppose that $n$ is a positive integer such that in base $7$, then $n$ can be expressed as $\overline{ABC}_7$, and in base $11$, then $n$ can be expressed as $\overline{CBA}_{11}$. Find the largest possible value of $n$ in base $10$.
Suppose that $n$ is a positive integer such that in base $7$, then $n$ can be expressed as $\overline{ABC}_7$, and in base $11$, then $n$ can be expressed as $\overline{CBA}_{11}$. Find the largest possible value of $n$ in base $10$.
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Answered by
oobleck
was something wrong with the solution I proposed before? Here it is again.
what do we have?
49a + 7b + c = 121c + 11b + a
or, equivalently,
b = 12a - 30c
So, one solution is 361<sub><sub>7</sub></sub> = 163<sub><sub>11</sub></sub> = 190<sub><sub>10</sub></sub>
Since all of a,b,c must be from 1 to 6 (since abc must be expressible in base 7), it shouldn't take too long to explore all the possibilities.
what do we have?
49a + 7b + c = 121c + 11b + a
or, equivalently,
b = 12a - 30c
So, one solution is 361<sub><sub>7</sub></sub> = 163<sub><sub>11</sub></sub> = 190<sub><sub>10</sub></sub>
Since all of a,b,c must be from 1 to 6 (since abc must be expressible in base 7), it shouldn't take too long to explore all the possibilities.
Answered by
Charles
@oobleck, there is a larger value to the equeation
Answered by
oobleck
ok. I trust that you worked until you found it. There aren't that many possibilities to try. 36 max, using all 6 possible values for a and c.
Answered by
Charles
No, in inputted it into my thing, and it said wrong
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