document.write( "Question 1207584: Let $N$ be a positive integer. The number $N$ has three digits when expressed in base $7$. When the number $N$ is expressed in base $12$, it has the same three digits, in reverse order. What is $N$? (Express your answer in decimal.) \n" ); document.write( "
Algebra.Com's Answer #845545 by math_tutor2020(3817)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "I agree with tutor greenestamps.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To verify I wrote a quick python script to check numbers 100 through 666 in base 7.
\n" ); document.write( "The script couldn't find any solutions, but it did find these near-misses
\n" ); document.write( "300 base 7 = 103 base 12
\n" ); document.write( "301 base 7 = 104 base 12
\n" ); document.write( "which is a bit interesting.\r
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\n" ); document.write( "\n" ); document.write( "I found a similar problem online dealing with bases 11 and 15.
\n" ); document.write( "The python script found that:
\n" ); document.write( "241 base 11 = 142 base 15
\n" ); document.write( "482 base 11 = 284 base 15\r
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\n" ); document.write( "\n" ); document.write( "Furthermore,
\n" ); document.write( "204 base 7 = 402 base 5
\n" ); document.write( "102 base 7 = 201 base 5
\n" ); document.write( "and
\n" ); document.write( "361 base 7 = 163 base 11
\n" ); document.write( "502 base 7 = 205 base 11\r
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\n" ); document.write( "\n" ); document.write( "There are likely many other pairs of values like this.
\n" ); document.write( "It's possible your teacher made a typo somewhere.
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