document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151144>Question 1151144</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Five integers between 440 and 500 can each be expressed as the sum of two<BR>\n" );
document.write( "different squares in two different ways. Find their median.  </SPAN>\n" );
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document.write( "The 5 numbers that meet the description are <font color=\"blue\">442, 445, 481, 485, 493</font>\r<BR>\n" );
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document.write( "Based on what is shown below:<BR>\n" );
document.write( "1^2 + 21^2 = 1 + 441 = <font color=\"blue\">442</font><BR>\n" );
document.write( "9^2 + 19^2 = 81 + 361 = <font color=\"blue\">442</font><BR>\n" );
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document.write( "2^2 + 21^2 = 4 + 441 = <font color=\"blue\">445</font><BR>\n" );
document.write( "11^2 + 18^2 = 121 + 324 = <font color=\"blue\">445</font><BR>\n" );
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document.write( "9^2 + 20^2 = 81 + 400 = <font color=\"blue\">481</font><BR>\n" );
document.write( "15^2 + 16^2 = 225 + 256 = <font color=\"blue\">481</font><BR>\n" );
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document.write( "1^2 + 22^2 = 1 + 484 = <font color=\"blue\">485</font><BR>\n" );
document.write( "14^2 + 17^2 = 196 + 289 = <font color=\"blue\">485</font><BR>\n" );
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document.write( "3^2 + 22^2 = 9 + 484 = <font color=\"blue\">493</font><BR>\n" );
document.write( "13^2 + 18^2 = 169 + 324 = <font color=\"blue\">493</font><BR>\n" );
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document.write( "I used a perl script to search for all the integers between 440 and 500, excluding the endpoints (see note below), such that the integer could be broken down into a sum of two distinct squares.\r<BR>\n" );
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document.write( "Note: we can express 500 as a sum of two different squares in two different ways<BR>\n" );
document.write( "4^2 + 22^2 = 16 + 484 = 500<BR>\n" );
document.write( "10^2 + 20^2 = 100 + 400 = 500<BR>\n" );
document.write( "but that would mean we're dealing with 6 values instead of 5. So it appears we are ignoring the endpoints 440 and 500. \r<BR>\n" );
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document.write( "We are also ignoring 450<BR>\n" );
document.write( "3^2 + 21^2 = 9+441 = 450<BR>\n" );
document.write( "15^2 + 15^2 = 225+225 = 450<BR>\n" );
document.write( "because the second summation line has us adding the same square to itself, ie we dont have two distinct square numbers here. \r<BR>\n" );
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document.write( "Once again the five numbers are: <font color=\"blue\">442, 445, 481, 485, 493</font>\r<BR>\n" );
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document.write( "The median is the middle most value. In this case, it would be the value in the third slot.\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>481</font><BR>\n" );
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