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\n" ); document.write( "One of the other tutors understood the poorly posed problem correctly and showed a good formal solution.
\n" ); document.write( "If finding the answer quickly is important and a formal mathematical solution is not required, you can find the answer with a little bit of mental arithmetic.
\n" ); document.write( "The problem would not make any sense if n were not an integer, so do some estimating to find the probable answer and then verify that answer.
\n" ); document.write( "1022 base 4 is a bit more than 4^3=64; 244 base n is between 2n^2 and 3n^2. Some quick mental calculations show the probable answer is n=5.
\n" ); document.write( "Now confirm that answer.
\n" ); document.write( "1022 base 4 = 64+2(4)+2 = 74
\n" ); document.write( "244 base 5 = 2(25)+4(5)+4 = 74
\n" ); document.write( "ANSWER: n=5
\n" ); document.write( "NOTE: For a student familiar with numbers in bases other than base 10, here is another way to evaluate 244 base 5:
\n" ); document.write( "244 base 5 = (300-1) base 5 = 3(25)-1 = 75-1 = 74
\n" ); document.write( "That method works because 4 is the largest digit in base 5, so the next number after 244 in base 5 is 300.
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