document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170287>Question 170287</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What's my telephone number? (_ _ _) _ _ _ - _ _ _ _\r<BR>\n" );
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document.write( "Each digit is different.\r<BR>\n" );
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document.write( "The Product of the sixth and seventh numbers is the third number.\r<BR>\n" );
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document.write( "The fourth, eigth, ninth, and tenth numbers are multiples of 3.\r<BR>\n" );
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document.write( "The sum of the fourth and sixth numbers is the same as the sum of the fifth and eigth numbers.\r<BR>\n" );
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document.write( "The second, third, sixth, and seventh numbers are powers of 2.\r<BR>\n" );
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document.write( "The first, fifth, seventh, and tenth numbers are prime.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125701 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=125701\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: I'm going to let a=first digit, b=second digit, c=third digit etc, until I get to j=tenth digit\r<BR>\n" );
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document.write( "So the telephone number looks like this:\r<BR>\n" );
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document.write( "(a b c) d e f - g h i j\r<BR>\n" );
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document.write( "Now let's do some translations:\r<BR>\n" );
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document.write( "\"The Product of the sixth and seventh numbers is the third number. \" \r<BR>\n" );
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document.write( "translates to\r<BR>\n" );
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document.write( "f*g=c\r<BR>\n" );
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document.write( "--------------------\r<BR>\n" );
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document.write( "\"The fourth, eigth, ninth, and tenth numbers are multiples of 3\"\r<BR>\n" );
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document.write( "translates to \r<BR>\n" );
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document.write( "d, h, i, j are multiples of 3 (giving us the possible values 0, 3, 6, 9)\r<BR>\n" );
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document.write( "Note: 0 is a multiple since 3*0=0\r<BR>\n" );
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document.write( "--------------------\r<BR>\n" );
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document.write( "\"The sum of the fourth and sixth numbers is the same as the sum of the fifth and eigth numbers. \"\r<BR>\n" );
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document.write( "translates to\r<BR>\n" );
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document.write( "d+f = e+h\r<BR>\n" );
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document.write( "--------------------\r<BR>\n" );
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document.write( "\"The second, third, sixth, and seventh numbers are powers of 2.\"\r<BR>\n" );
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document.write( "translates to\r<BR>\n" );
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document.write( "b, c, f, g are powers of 2 which gives the possible values: 1, 2, 4, 8\r<BR>\n" );
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document.write( "Note: 1 is a power of 2 since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E0=1 ALIGN=MIDDLE  ALT=\"2%5E0=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "--------------------\r<BR>\n" );
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document.write( "\"The first, fifth, seventh, and tenth numbers are prime.\"\r<BR>\n" );
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document.write( "translates to\r<BR>\n" );
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document.write( "a, e, g, j are prime \r<BR>\n" );
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document.write( "List of (single digit) prime numbers: 2, 3, 5, 7\r<BR>\n" );
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document.write( "You will need to refer back to this list so it might help to write the list on a separate sheet of paper and cross out any digits that we've used\r<BR>\n" );
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document.write( "===============================================================\r<BR>\n" );
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document.write( "Note: remember, each digit is different which means that NO repeats are allowed.\r<BR>\n" );
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document.write( "Since digit j is both a multiple of 3 AND is prime, this means that the only possible digit for j is 3 (since 3 is both a multiple of 3 AND prime)\r<BR>\n" );
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document.write( "So <font color=\"red\">j=3</font>\r<BR>\n" );
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document.write( "The same can be done with g. Since g is both a power of 2 AND is prime, the only candidate is 2 (since 2 is both a power of 2 AND is prime)\r<BR>\n" );
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document.write( "So <font color=\"red\">g=2</font>\r<BR>\n" );
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document.write( "Looking at f*g=c, we know that all three are powers of 2. So this means that f*2=some power of 2\r<BR>\n" );
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document.write( "So let's try some values of f\r<BR>\n" );
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document.write( "f=1 (CANNOT do since 1*2=2; a repeat would occur where g=c)<BR>\n" );
document.write( "f=2 (CANNOT do since 2 is already taken)<BR>\n" );
document.write( "f=4 (CAN do since 4*2=8; all three are powers of 2)<BR>\n" );
document.write( "f=8 (CANNOT do since 8*2=16; 16 is comprised of 2 digits)\r<BR>\n" );
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document.write( "So <font color=\"red\">f=4</font> and <font color=\"red\">c=8</font>\r<BR>\n" );
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document.write( "Since we know that <font color=\"red\">g=2</font>, <font color=\"red\">f=4</font>, and <font color=\"red\">c=8</font> (and there are ONLY 4 digits that are powers of 2), this means that <font color=\"red\">b=1</font> (by elimination)\r<BR>\n" );
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document.write( "Just to recap, we've taken the digits 3, 2, 4, 8, and 1 so far (5 digits taken already).\r<BR>\n" );
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document.write( "--------------------------------------\r<BR>\n" );
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document.write( "Now let's move onto the equation \r<BR>\n" );
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document.write( "d+f = e+h\r<BR>\n" );
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document.write( "We know that f=4, so let's plug that in:\r<BR>\n" );
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document.write( "d+4 = e+h\r<BR>\n" );
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document.write( "Here's where we have to try some combinations\r<BR>\n" );
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document.write( "The possible values for d are 0, 6, and 9 (remember d is a multiple of 3 and the digit 3 is already taken)\r<BR>\n" );
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document.write( "The possible values for e are 5 and 7 (e is prime and the digits 2 and 3 are already taken)\r<BR>\n" );
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document.write( "The possible values for h are 0, 6, and 9 (remember h is a multiple of 3 and the digit 3 is already taken)\r<BR>\n" );
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document.write( "So we could have the following:\r<BR>\n" );
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document.write( "d=0 OR d=6 OR d=9\r<BR>\n" );
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document.write( "e=5 OR e=7\r<BR>\n" );
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document.write( "h=0 OR h=6 OR h=9\r<BR>\n" );
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document.write( "So let's add some combinations:\r<BR>\n" );
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document.write( "Combination 1:\r<BR>\n" );
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document.write( "If d=0, e=5, and h=6 (0 already taken), then\r<BR>\n" );
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document.write( "0+4=5+6<BR>\n" );
document.write( "4=11 ... which is false (cross this combination out)\r<BR>\n" );
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document.write( "Combination 2:\r<BR>\n" );
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document.write( "If d=0, e=5, and h=9, then\r<BR>\n" );
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document.write( "0+4=5+9<BR>\n" );
document.write( "4=14 ... which is false (cross this combination out)\r<BR>\n" );
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document.write( "Combination 3:\r<BR>\n" );
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document.write( "If d=0, e=7, and h=6 (0 already taken), then\r<BR>\n" );
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document.write( "0+4=7+6<BR>\n" );
document.write( "4=13 ... which is false (cross this combination out)\r<BR>\n" );
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document.write( "Combination 4:\r<BR>\n" );
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document.write( "If d=0, e=7, and h=9, then\r<BR>\n" );
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document.write( "0+4=7+9<BR>\n" );
document.write( "4=16 ... which is false (cross this combination out)\r<BR>\n" );
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document.write( "Combination 4:\r<BR>\n" );
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document.write( "If d=6, e=5, and h=0 (6 already taken), then\r<BR>\n" );
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document.write( "6+4=5+0<BR>\n" );
document.write( "10=5 ... which is false (cross this combination out)\r<BR>\n" );
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document.write( "Combination 5:\r<BR>\n" );
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document.write( "If d=6, e=5, and h=9 (6 already taken), then\r<BR>\n" );
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document.write( "6+4=5+6<BR>\n" );
document.write( "10=11 ... which is false (cross this combination out)\r<BR>\n" );
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document.write( "Combination 6:\r<BR>\n" );
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document.write( "If d=6, e=7, and h=0 (6 already taken), then\r<BR>\n" );
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document.write( "6+4=7+0<BR>\n" );
document.write( "10=7 ... which is false (cross this combination out)\r<BR>\n" );
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document.write( "Combination 7:\r<BR>\n" );
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document.write( "If d=6, e=7, and h=9 (6 already taken), then\r<BR>\n" );
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document.write( "6+4=7+9<BR>\n" );
document.write( "10=16 ... which is false (cross this combination out)\r<BR>\n" );
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document.write( "Combination 8:\r<BR>\n" );
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document.write( "If d=9, e=7, and h=0 (9 already taken), then\r<BR>\n" );
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document.write( "9+4=7+0<BR>\n" );
document.write( "13=7 ... which is false (cross this combination out)\r<BR>\n" );
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document.write( "Combination 9:\r<BR>\n" );
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document.write( "If d=9, e=7, and h=6 (9 already taken), then\r<BR>\n" );
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document.write( "9+4=7+6<BR>\n" );
document.write( "13=13 ... which works\r<BR>\n" );
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document.write( "So after trying 8 combinations of numbers, we get\r<BR>\n" );
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document.write( "<font color=\"red\">d=9</font>, <font color=\"red\">e=7</font> and <font color=\"red\">h=6</font>\r<BR>\n" );
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document.write( "-----------------------------------------------------------\r<BR>\n" );
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document.write( "So to recap, we've taken the digits 3, 2, 4, 1, and 8 (from the first part) and the digits 9, 7, and 6 (from the second part)\r<BR>\n" );
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document.write( "Altogether, we know that \r<BR>\n" );
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document.write( "<font color=\"red\">j=3</font>, <font color=\"red\">g=2</font>, <font color=\"red\">f=4</font>, <font color=\"red\">b=1</font>, and <font color=\"red\">c=8</font> (from part 1)\r<BR>\n" );
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document.write( "<font color=\"red\">d=9</font>, <font color=\"red\">e=7</font> and <font color=\"red\">h=6</font> (from part 2)\r<BR>\n" );
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document.write( "------------------------------------------------------\r<BR>\n" );
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document.write( "Since <font color=\"red\">d=9</font>, <font color=\"red\">h=6</font>, and <font color=\"red\">j=3</font>, using elimination we get <font color=\"red\">i=0</font> (note: I'm looking at the \"multiples of 3\" group)\r<BR>\n" );
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document.write( "Finally, since <font color=\"red\">e=7</font>, <font color=\"red\">g=2</font>, and <font color=\"red\">j=3</font>, this means that <font color=\"red\">a=5</font> (note: I'm looking at the \"prime numbers\" group)\r<BR>\n" );
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document.write( "================================================================\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So we have the following numbers:\r<BR>\n" );
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document.write( "<font color=\"red\">a=5</font><BR>\n" );
document.write( "<font color=\"red\">b=1</font><BR>\n" );
document.write( "<font color=\"red\">c=8</font>\r<BR>\n" );
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document.write( "<font color=\"red\">d=9</font><BR>\n" );
document.write( "<font color=\"red\">e=7</font><BR>\n" );
document.write( "<font color=\"red\">f=4</font>\r<BR>\n" );
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document.write( "<font color=\"red\">g=2</font><BR>\n" );
document.write( "<font color=\"red\">h=6</font><BR>\n" );
document.write( "<font color=\"red\">i=0</font><BR>\n" );
document.write( "<font color=\"red\">j=3</font>\r<BR>\n" );
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document.write( "which means that the telephone number is \r<BR>\n" );
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document.write( "(518) 974-2603\r<BR>\n" );
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