document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=835054>Question 835054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using every one of the digits 1-9 only once, make an addition problem using only 3-digit numbers.  I made a systematic list of all three digit answers from 981 to 459 and could find addends to sum to all of those answers except for 864, 765, and 756. Why don't these 3 work and why don't numbers in the 300s work? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #503395 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=503395\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "There is no system that will guarantee that\r\n" );
document.write( "you don't use any digits more than once.  \r\n" );
document.write( "You can use any of these 168 ways.  I found\r\n" );
document.write( "these by a computer program.\r\n" );
document.write( "\r\n" );
document.write( " 1.  124 + 659 = 783\r\n" );
document.write( " 2.  125 + 739 = 864\r\n" );
document.write( " 3.  127 + 359 = 486\r\n" );
document.write( " 4.  127 + 368 = 495\r\n" );
document.write( " 5.  128 + 367 = 495\r\n" );
document.write( " 6.  128 + 439 = 567\r\n" );
document.write( " 7.  129 + 357 = 486\r\n" );
document.write( " 8.  129 + 438 = 567\r\n" );
document.write( " 9.  129 + 654 = 783\r\n" );
document.write( "10.  129 + 735 = 864\r\n" );
document.write( "11.  134 + 658 = 792\r\n" );
document.write( "12.  135 + 729 = 864\r\n" );
document.write( "13.  138 + 429 = 567\r\n" );
document.write( "14.  138 + 654 = 792\r\n" );
document.write( "15.  139 + 428 = 567\r\n" );
document.write( "16.  139 + 725 = 864\r\n" );
document.write( "17.  142 + 596 = 738\r\n" );
document.write( "18.  142 + 695 = 837\r\n" );
document.write( "19.  143 + 586 = 729\r\n" );
document.write( "20.  145 + 692 = 837\r\n" );
document.write( "21.  146 + 583 = 729\r\n" );
document.write( "22.  146 + 592 = 738\r\n" );
document.write( "23.  152 + 487 = 639\r\n" );
document.write( "24.  152 + 784 = 936\r\n" );
document.write( "25.  154 + 629 = 783\r\n" );
document.write( "26.  154 + 638 = 792\r\n" );
document.write( "27.  154 + 782 = 936\r\n" );
document.write( "28.  157 + 329 = 486\r\n" );
document.write( "29.  157 + 482 = 639\r\n" );
document.write( "30.  158 + 634 = 792\r\n" );
document.write( "31.  159 + 327 = 486\r\n" );
document.write( "32.  159 + 624 = 783\r\n" );
document.write( "33.  162 + 387 = 549\r\n" );
document.write( "34.  162 + 783 = 945\r\n" );
document.write( "35.  163 + 782 = 945\r\n" );
document.write( "36.  167 + 328 = 495\r\n" );
document.write( "37.  167 + 382 = 549\r\n" );
document.write( "38.  168 + 327 = 495\r\n" );
document.write( "39.  173 + 286 = 459\r\n" );
document.write( "40.  173 + 295 = 468\r\n" );
document.write( "41.  175 + 293 = 468\r\n" );
document.write( "42.  176 + 283 = 459\r\n" );
document.write( "43.  182 + 367 = 549\r\n" );
document.write( "44.  182 + 394 = 576\r\n" );
document.write( "45.  182 + 457 = 639\r\n" );
document.write( "46.  182 + 493 = 675\r\n" );
document.write( "47.  182 + 754 = 936\r\n" );
document.write( "48.  182 + 763 = 945\r\n" );
document.write( "49.  183 + 276 = 459\r\n" );
document.write( "50.  183 + 492 = 675\r\n" );
document.write( "51.  183 + 546 = 729\r\n" );
document.write( "52.  183 + 762 = 945\r\n" );
document.write( "53.  184 + 392 = 576\r\n" );
document.write( "54.  184 + 752 = 936\r\n" );
document.write( "55.  186 + 273 = 459\r\n" );
document.write( "56.  186 + 543 = 729\r\n" );
document.write( "57.  187 + 362 = 549\r\n" );
document.write( "58.  187 + 452 = 639\r\n" );
document.write( "59.  192 + 384 = 576\r\n" );
document.write( "60.  192 + 483 = 675\r\n" );
document.write( "61.  192 + 546 = 738\r\n" );
document.write( "62.  192 + 645 = 837\r\n" );
document.write( "63.  193 + 275 = 468\r\n" );
document.write( "64.  193 + 482 = 675\r\n" );
document.write( "65.  194 + 382 = 576\r\n" );
document.write( "66.  195 + 273 = 468\r\n" );
document.write( "67.  195 + 642 = 837\r\n" );
document.write( "68.  196 + 542 = 738\r\n" );
document.write( "69.  214 + 569 = 783\r\n" );
document.write( "70.  214 + 659 = 873\r\n" );
document.write( "71.  215 + 478 = 693\r\n" );
document.write( "72.  215 + 748 = 963\r\n" );
document.write( "73.  216 + 378 = 594\r\n" );
document.write( "74.  216 + 738 = 954\r\n" );
document.write( "75.  218 + 349 = 567\r\n" );
document.write( "76.  218 + 376 = 594\r\n" );
document.write( "77.  218 + 439 = 657\r\n" );
document.write( "78.  218 + 475 = 693\r\n" );
document.write( "79.  218 + 736 = 954\r\n" );
document.write( "80.  218 + 745 = 963\r\n" );
document.write( "81.  219 + 348 = 567\r\n" );
document.write( "82.  219 + 438 = 657\r\n" );
document.write( "83.  219 + 564 = 783\r\n" );
document.write( "84.  219 + 654 = 873\r\n" );
document.write( "85.  234 + 657 = 891\r\n" );
document.write( "86.  235 + 746 = 981\r\n" );
document.write( "87.  236 + 718 = 954\r\n" );
document.write( "88.  236 + 745 = 981\r\n" );
document.write( "89.  237 + 654 = 891\r\n" );
document.write( "90.  238 + 419 = 657\r\n" );
document.write( "91.  238 + 716 = 954\r\n" );
document.write( "92.  239 + 418 = 657\r\n" );
document.write( "93.  241 + 596 = 837\r\n" );
document.write( "94.  243 + 576 = 819\r\n" );
document.write( "95.  243 + 675 = 918\r\n" );
document.write( "96.  245 + 673 = 918\r\n" );
document.write( "97.  245 + 718 = 963\r\n" );
document.write( "98.  245 + 736 = 981\r\n" );
document.write( "99.  246 + 573 = 819\r\n" );
document.write( "100.  246 + 591 = 837\r\n" );
document.write( "101.  246 + 735 = 981\r\n" );
document.write( "102.  248 + 319 = 567\r\n" );
document.write( "103.  248 + 715 = 963\r\n" );
document.write( "104.  249 + 318 = 567\r\n" );
document.write( "105.  251 + 397 = 648\r\n" );
document.write( "106.  254 + 619 = 873\r\n" );
document.write( "107.  254 + 637 = 891\r\n" );
document.write( "108.  257 + 391 = 648\r\n" );
document.write( "109.  257 + 634 = 891\r\n" );
document.write( "110.  259 + 614 = 873\r\n" );
document.write( "111.  264 + 519 = 783\r\n" );
document.write( "112.  269 + 514 = 783\r\n" );
document.write( "113.  271 + 593 = 864\r\n" );
document.write( "114.  271 + 683 = 954\r\n" );
document.write( "115.  273 + 546 = 819\r\n" );
document.write( "116.  273 + 591 = 864\r\n" );
document.write( "117.  273 + 645 = 918\r\n" );
document.write( "118.  273 + 681 = 954\r\n" );
document.write( "119.  275 + 418 = 693\r\n" );
document.write( "120.  275 + 643 = 918\r\n" );
document.write( "121.  276 + 318 = 594\r\n" );
document.write( "122.  276 + 543 = 819\r\n" );
document.write( "123.  278 + 316 = 594\r\n" );
document.write( "124.  278 + 415 = 693\r\n" );
document.write( "125.  281 + 394 = 675\r\n" );
document.write( "126.  281 + 673 = 954\r\n" );
document.write( "127.  283 + 671 = 954\r\n" );
document.write( "128.  284 + 391 = 675\r\n" );
document.write( "129.  291 + 357 = 648\r\n" );
document.write( "130.  291 + 384 = 675\r\n" );
document.write( "131.  291 + 546 = 837\r\n" );
document.write( "132.  291 + 573 = 864\r\n" );
document.write( "133.  293 + 571 = 864\r\n" );
document.write( "134.  294 + 381 = 675\r\n" );
document.write( "135.  296 + 541 = 837\r\n" );
document.write( "136.  297 + 351 = 648\r\n" );
document.write( "137.  314 + 658 = 972\r\n" );
document.write( "138.  317 + 529 = 846\r\n" );
document.write( "139.  317 + 628 = 945\r\n" );
document.write( "140.  318 + 627 = 945\r\n" );
document.write( "141.  318 + 654 = 972\r\n" );
document.write( "142.  319 + 527 = 846\r\n" );
document.write( "143.  324 + 567 = 891\r\n" );
document.write( "144.  324 + 657 = 981\r\n" );
document.write( "145.  327 + 519 = 846\r\n" );
document.write( "146.  327 + 564 = 891\r\n" );
document.write( "147.  327 + 618 = 945\r\n" );
document.write( "148.  327 + 654 = 981\r\n" );
document.write( "149.  328 + 617 = 945\r\n" );
document.write( "150.  329 + 517 = 846\r\n" );
document.write( "151.  341 + 586 = 927\r\n" );
document.write( "152.  342 + 576 = 918\r\n" );
document.write( "153.  346 + 572 = 918\r\n" );
document.write( "154.  346 + 581 = 927\r\n" );
document.write( "155.  352 + 467 = 819\r\n" );
document.write( "156.  354 + 618 = 972\r\n" );
document.write( "157.  354 + 627 = 981\r\n" );
document.write( "158.  357 + 462 = 819\r\n" );
document.write( "159.  357 + 624 = 981\r\n" );
document.write( "160.  358 + 614 = 972\r\n" );
document.write( "161.  362 + 457 = 819\r\n" );
document.write( "162.  364 + 527 = 891\r\n" );
document.write( "163.  367 + 452 = 819\r\n" );
document.write( "164.  367 + 524 = 891\r\n" );
document.write( "165.  372 + 546 = 918\r\n" );
document.write( "166.  376 + 542 = 918\r\n" );
document.write( "167.  381 + 546 = 927\r\n" );
document.write( "168.  386 + 541 = 927\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin</PRE> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );