document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136994>Question 1136994</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Reading from left to right, a sequence consists of 6 X’s, followed by 24 Y’s, followed<BR>\n" );
document.write( "by 96 X’s. After the first n letters, reading from left to right, one letter has occurred<BR>\n" );
document.write( "twice as many times as the other letter. The sum of the four possible values of n is? </SPAN>\n" );
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document.write( "Figure it out on your own -- it's good exercise for the brain:<br><BR>\n" );
document.write( "(1) The first n is when the first 6 X's are twice the total number of Y's.<BR>\n" );
document.write( "(2) The second n is when the first 6 X's are half as many as the number of Y's.<BR>\n" );
document.write( "(3) The third n is when all 24 Y's are twice the number of X's.<BR>\n" );
document.write( "(4) The fourth n is when all 24 Y's are half the total number of X's.<br><BR>\n" );
document.write( "Add the four values of n....<br><BR>\n" );
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document.write( "The thought process, in more detail....<br><BR>\n" );
document.write( "Think about writing out the string of letters, one letter at a time.  You are looking for times when the number of X's is twice the number of Y's, or the number of Y's is twice the number of X's.<br><BR>\n" );
document.write( "The first 6 letters are all X's; after that you write a bunch of Y's.<BR>\n" );
document.write( "How many Y's do you write before the number of X's is twice the number of Y's?<BR>\n" );
document.write( "There are 6 X's, so you need 3 Y's.<BR>\n" );
document.write( "So when the total number of letters in the string is 6+3=9, there are twice as many X's as Y's.  So the first value of n you are looking for is 9.<br><BR>\n" );
document.write( "Now you continue writing more Y's.  The number of X's stays at 6, while the number of Y's increases.<BR>\n" );
document.write( "At some point, the number of Y's will be twice the number of X's.<BR>\n" );
document.write( "When will that happen?  There are 6 X's at the beginning of the string; when the number of Y's reaches 12, there will be twice as many Y's as X's.<BR>\n" );
document.write( "So when the total number of letters in the string is 6+12=18, the number of Y's will be twice the number of X's.  So the second value of n you are looking for is 6+12 = 18.<br><BR>\n" );
document.write( "Continue adding letters to figure out the last two values of n.<br><BR>\n" );
document.write( "After the first 6 X's in the string, there are 24Y's; then you start writing more X's, with the number of Y's staying at 24.<br><BR>\n" );
document.write( "As you write more X's with the number of Y's staying at 24, you will first reach a point where the number of Y's (24) is twice the total number of X's; then, as you write still more X's, you will reach a point where the number of X's is twice the number of Y's (which is still 24). </SPAN>\n" );
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