document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208179>Question 1208179</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 4+5 = 3 , 7 × 7 = 7 , 40-4 = 6 then 45 + 5 = ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846416 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=846416\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( " If 4+5 = 3 , 7 × 7 = 7 , 40-4 = 6 then 45 + 5 = ?<BR>\n" );
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document.write( "                           It is easy.\r\n" );
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document.write( "In this problem, the signs of arithmetic operations are not usual/traditional \r\n" );
document.write( "addition, multiplication, subtraction,\r\n" );
document.write( "to which you are familiar from school years.\r\n" );
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document.write( "They are special operations: their meaning is \r\n" );
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document.write( "    +----------------------------------------------------+\r\n" );
document.write( "    |  make a traditional operation with the arguments;  |\r\n" );
document.write( "    |  then take the square root from the resultant.     |\r\n" );
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document.write( "Indeed, if you take the sum of 4+5, you will get 9;\r\n" );
document.write( "        when you take square root from  9, you will get 3.\r\n" );
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document.write( "        If you take the product  7 * 7, you will get 49;\r\n" );
document.write( "        when you take square root from  49, you will get 7.\r\n" );
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document.write( "        If you subtract  4 from 40, you will get 36;\r\n" );
document.write( "        when you take square root from  36, you will get 6.\r\n" );
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document.write( "As you see, this interpretation works in all three given cases:\r\n" );
document.write( "they are pre-requisites to establish the rule.\r\n" );
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document.write( "Now we apply the rule to 45 + 5.  We first add and get 50;\r\n" );
document.write( "                                  then we take square root of 50 and get the\r\n" );
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document.write( "<U>ANSWER</U>.  For this operation, 45 + 5,  the output is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "As to me, it seems very logical;  so, I believe in it.\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "The proper mathematical formulation for this problem is as follows:\r<BR>\n" );
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document.write( "    Create an appropriate interpretation of arithmetical operations\r\n" );
document.write( "      in a way that the given equalities be proper; then compute\r\n" );
document.write( "                        the last output.\r\n" );
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document.write( "/////////////// - - - A refutation with full explanation - - - \\\\\\\\\\\\\\\\\r<BR>\n" );
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document.write( "Surely, this problem is not a Math problem - it is a puzzle.\r<BR>\n" );
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document.write( "It is a puzzle of that kind that have no mathematical solution inside traditional mathematical logic.\r<BR>\n" );
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document.write( "What I wrote above and presented as a solution, was simply a joke from my side.\r<BR>\n" );
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document.write( "Why people spend their time to \"solve\" such puzzles that have no logical solution ?<BR>\n" );
document.write( "- Mostly to kill their time without getting back any benefits.\r<BR>\n" );
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document.write( "Why people do it ? - There are many reasons for it.<BR>\n" );
document.write( "One of the reasons is that there are many people in the word, who desire,<BR>\n" );
document.write( "from time to time, to kill their time, because they have nothing to do.<BR>\n" );
document.write( "Many of these people are fully or almost fully illiterate in Math.\r<BR>\n" );
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document.write( "Therefore, from one side, they can not solve Math problems to develop their mind,<BR>\n" );
document.write( "but still feel the necessity to kill their time - so, they solve puzzles.\r<BR>\n" );
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document.write( "In 90% of cases, they even can not solve puzzles, too; therefore, they post them <BR>\n" );
document.write( "in the Internet to get the solutions from there.\r<BR>\n" );
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document.write( "These solutions only <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28IMITATE%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28IMITATE%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > proper mathematical logic, but these people can not distinct<BR>\n" );
document.write( "a proper Math logic from imitated logic - making this distinction is above their skills and understanding.\r<BR>\n" );
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document.write( "When they obtain absurdist solutions to their puzzles, they are very satisfied, because they see<BR>\n" );
document.write( "that other people around are equally stupid in Math and in the logic, as they themselves are.\r<BR>\n" );
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document.write( "- - - This way, the complete satisfaction comes - and complete grace descends from heaven - - - \r<BR>\n" );
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document.write( "So, I'd like repeat what I just said above - this \"problem\" is a puzzle; it is not a Math problem;<BR>\n" );
document.write( "my \"solution\" to this problem above was a joke; this kind of puzzles are mathematically nonsensical;<BR>\n" );
document.write( "they do not develop any skills, but serve for several purposes;\r<BR>\n" );
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document.write( "- First purpose is to help people to kill their time.<BR>\n" );
document.write( "- Second purpose is to enrich those people who create such puzzles in the Internet in their web-sites.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This is the harsh truth of life.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Good buy and have a nice day !\r<BR>\n" );
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document.write( "These puzzles always remind me of the fox Alice and the cat Basilio <BR>\n" );
document.write( "from the fairy child tale story about the small wooden boy Buratino / (Pinocchio).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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