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\n" ); document.write( "The problem is this:
\n" ); document.write( "321 (base n) = 232 (base 7)
\n" ); document.write( "Informally....
\n" ); document.write( "In any base (where the numbers are defined), 321 is greater than 232; so if 321 (base n) is equal to 232 (base 7), then the base n must be less than 7.
\n" ); document.write( "So try n=6....
\n" ); document.write( "321 (base 6)
\n" ); document.write( "3*6=18; 18+2=20
\n" ); document.write( "20*6=120; 120+1=121
\n" ); document.write( "232 (base 7)
\n" ); document.write( "2*7=14; 14+3=17
\n" ); document.write( "17*7=119; 119+2=121
\n" ); document.write( "n=6 works!
\n" ); document.write( "ANSWER: n=6
\n" ); document.write( "Formally....
\n" ); document.write( "321 (base n) = 3n^2+2n+1
\n" ); document.write( "232 (base 7) = 2(7^2)+3(7)+2 = 98+21+2 = 121
\n" ); document.write( "3n^2+2n+1=121
\n" ); document.write( "3n^2+2n-120 = 0
\n" ); document.write( "(n-6)(3n+20) = 0
\n" ); document.write( "n=6 or n=-20/3
\n" ); document.write( "Obviously the negative fractional answer makes not sense. So
\n" ); document.write( "ANSWER: n=6
\n" ); document.write( " \n" ); document.write( "