document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=88730>Question 88730</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A test has 10 true/false questions.  How many different tests can be turned in to the teacher? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #64494 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=64494\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first question could be answered either true or false.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "If you answered true on the first question, you could answer either true or false on the<BR>\n" );
document.write( "second question. <BR>\n" );
document.write( ".<BR>\n" );
document.write( "If you answered false on the first question you could answer either true or false on the <BR>\n" );
document.write( "second question.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So after two questions you have four possible situations: <BR>\n" );
document.write( ".<BR>\n" );
document.write( "True & then True<BR>\n" );
document.write( "True & then False<BR>\n" );
document.write( "False & then True<BR>\n" );
document.write( "False & then False<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now for each of those 4 possibilities, you could answer either true or false on the third question.<BR>\n" );
document.write( "So after 3 questions you would have 8 possible test answers ... 4 * 2.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "And for each of the 8 possible answer situations on the third question, you can answer either<BR>\n" );
document.write( "true or false on the fourth question. This will give you 8 * 2 = 16 possible answers after<BR>\n" );
document.write( "the fourth question.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "By now you have probably noticed the pattern. Each additional question increases the number<BR>\n" );
document.write( "of possible answer configurations by a factor of 2.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "This pattern is reflected by the equation:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Number of different tests = 2^n<BR>\n" );
document.write( ".<BR>\n" );
document.write( "where n represents the number of questions on the test.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "If there were just 1 question on the test there would be 2^1 possible answers (either true<BR>\n" );
document.write( "or false). If there were 2 questions on the test, the number of possible answer combinations<BR>\n" );
document.write( "would be 2^2 or 4. Similarly for 3 questions there would be 2^3 = 8 possible combinations.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Extending on this pattern, for a 10 question test there would be 2^10 possible combinations<BR>\n" );
document.write( "of answers. And 2^10 = 1024 possible answer combinations. That means that the teacher<BR>\n" );
document.write( "could possibly receive 1024 tests that are all different by at least one answer.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this provides you with a way of figuring out a process for solving questions <BR>\n" );
document.write( "such as this one. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );