Is this possible? If so what is the answer!!
2006-10-27 17:28:32 · 7 answers · asked by skoot84 1 in Science & Mathematics ➔ Mathematics
You cannot Carry over number!! This is still possible but how?
2006-10-27 17:52:11 · update #1
It is not possible without carry overs!
Yes, the key is to realize that in the digits 1-9 there are 5 odd numbers 1,3,5,7,9 and and only 4 even(2,4,6,8). Since no carry overs are allowed, the two 1s digits must sum to the 3rd. This must be true for the 10s and 100s digits also. So we have a set of three equations. For example, if in the 3 equations below, where e represents an even number and o is odd, the digits 1-9 were used exactly once as follows
o+o=e
o+o=e
o+e=o
then you would have 6 odds and 3 evens, which is no good since we must use 5 odds and 4 evens.
It is easy to see why it is not possible: You cannot have e+e=e since you would only have 1 e left and 5 odds, so you would necessarily end up with o+o=o, which is impossible. Therefore you can only have one e in each of the 3 equations, which would leave you one e short.
Pascal did a great job though it's a bit lengthy. Make sure you give all restrictions otherwise Pascal and others will waste their time.
2006-10-27 19:24:31 · answer #1 · answered by Jimbo 5 · 2⤊ 0⤋
There are 336 possible answers. They are:
124 + 659 = 783, 125 + 739 = 864, 127 + 359 = 486,
127 + 368 = 495, 128 + 367 = 495, 128 + 439 = 567,
129 + 357 = 486, 129 + 438 = 567, 129 + 654 = 783,
129 + 735 = 864, 134 + 658 = 792, 135 + 729 = 864,
138 + 429 = 567, 138 + 654 = 792, 139 + 428 = 567,
139 + 725 = 864, 142 + 596 = 738, 142 + 695 = 837,
143 + 586 = 729, 145 + 692 = 837, 146 + 583 = 729,
146 + 592 = 738, 152 + 487 = 639, 152 + 784 = 936,
154 + 629 = 783, 154 + 638 = 792, 154 + 782 = 936,
157 + 329 = 486, 157 + 482 = 639, 158 + 634 = 792,
159 + 327 = 486, 159 + 624 = 783, 162 + 387 = 549,
162 + 783 = 945, 163 + 782 = 945, 167 + 328 = 495,
167 + 382 = 549, 168 + 327 = 495, 173 + 286 = 459,
173 + 295 = 468, 175 + 293 = 468, 176 + 283 = 459,
182 + 367 = 549, 182 + 394 = 576, 182 + 457 = 639,
182 + 493 = 675, 182 + 754 = 936, 182 + 763 = 945,
183 + 276 = 459, 183 + 492 = 675, 183 + 546 = 729,
183 + 762 = 945, 184 + 392 = 576, 184 + 752 = 936,
186 + 273 = 459, 186 + 543 = 729, 187 + 362 = 549,
187 + 452 = 639, 192 + 384 = 576, 192 + 483 = 675,
192 + 546 = 738, 192 + 645 = 837, 193 + 275 = 468,
193 + 482 = 675, 194 + 382 = 576, 195 + 273 = 468,
195 + 642 = 837, 196 + 542 = 738, 214 + 569 = 783,
214 + 659 = 873, 215 + 478 = 693, 215 + 748 = 963,
216 + 378 = 594, 216 + 738 = 954, 218 + 349 = 567,
218 + 376 = 594, 218 + 439 = 657, 218 + 475 = 693,
218 + 736 = 954, 218 + 745 = 963, 219 + 348 = 567,
219 + 438 = 657, 219 + 564 = 783, 219 + 654 = 873,
234 + 657 = 891, 235 + 746 = 981, 236 + 718 = 954,
236 + 745 = 981, 237 + 654 = 891, 238 + 419 = 657,
238 + 716 = 954, 239 + 418 = 657, 241 + 596 = 837,
243 + 576 = 819, 243 + 675 = 918, 245 + 673 = 918,
245 + 718 = 963, 245 + 736 = 981, 246 + 573 = 819,
246 + 591 = 837, 246 + 735 = 981, 248 + 319 = 567,
248 + 715 = 963, 249 + 318 = 567, 251 + 397 = 648,
254 + 619 = 873, 254 + 637 = 891, 257 + 391 = 648,
257 + 634 = 891, 259 + 614 = 873, 264 + 519 = 783,
269 + 514 = 783, 271 + 593 = 864, 271 + 683 = 954,
273 + 186 = 459, 273 + 195 = 468, 273 + 546 = 819,
273 + 591 = 864, 273 + 645 = 918, 273 + 681 = 954,
275 + 193 = 468, 275 + 418 = 693, 275 + 643 = 918,
276 + 183 = 459, 276 + 318 = 594, 276 + 543 = 819,
278 + 316 = 594, 278 + 415 = 693, 281 + 394 = 675,
281 + 673 = 954, 283 + 176 = 459, 283 + 671 = 954,
284 + 391 = 675, 286 + 173 = 459, 291 + 357 = 648,
291 + 384 = 675, 291 + 546 = 837, 291 + 573 = 864,
293 + 175 = 468, 293 + 571 = 864, 294 + 381 = 675,
295 + 173 = 468, 296 + 541 = 837, 297 + 351 = 648,
314 + 658 = 972, 316 + 278 = 594, 317 + 529 = 846,
317 + 628 = 945, 318 + 249 = 567, 318 + 276 = 594,
318 + 627 = 945, 318 + 654 = 972, 319 + 248 = 567,
319 + 527 = 846, 324 + 567 = 891, 324 + 657 = 981,
327 + 159 = 486, 327 + 168 = 495, 327 + 519 = 846,
327 + 564 = 891, 327 + 618 = 945, 327 + 654 = 981,
328 + 167 = 495, 328 + 617 = 945, 329 + 157 = 486,
329 + 517 = 846, 341 + 586 = 927, 342 + 576 = 918,
346 + 572 = 918, 346 + 581 = 927, 348 + 219 = 567,
349 + 218 = 567, 351 + 297 = 648, 352 + 467 = 819,
354 + 618 = 972, 354 + 627 = 981, 357 + 129 = 486,
357 + 291 = 648, 357 + 462 = 819, 357 + 624 = 981,
358 + 614 = 972, 359 + 127 = 486, 362 + 187 = 549,
362 + 457 = 819, 364 + 527 = 891, 367 + 128 = 495,
367 + 182 = 549, 367 + 452 = 819, 367 + 524 = 891,
368 + 127 = 495, 372 + 546 = 918, 376 + 218 = 594,
376 + 542 = 918, 378 + 216 = 594, 381 + 294 = 675,
381 + 546 = 927, 382 + 167 = 549, 382 + 194 = 576,
384 + 192 = 576, 384 + 291 = 675, 386 + 541 = 927,
387 + 162 = 549, 391 + 257 = 648, 391 + 284 = 675,
392 + 184 = 576, 394 + 182 = 576, 394 + 281 = 675,
397 + 251 = 648, 415 + 278 = 693, 418 + 239 = 657,
418 + 275 = 693, 419 + 238 = 657, 428 + 139 = 567,
429 + 138 = 567, 438 + 129 = 567, 438 + 219 = 657,
439 + 128 = 567, 439 + 218 = 657, 452 + 187 = 639,
452 + 367 = 819, 457 + 182 = 639, 457 + 362 = 819,
462 + 357 = 819, 467 + 352 = 819, 475 + 218 = 693,
478 + 215 = 693, 482 + 157 = 639, 482 + 193 = 675,
483 + 192 = 675, 487 + 152 = 639, 492 + 183 = 675,
493 + 182 = 675, 514 + 269 = 783, 517 + 329 = 846,
519 + 264 = 783, 519 + 327 = 846, 524 + 367 = 891,
527 + 319 = 846, 527 + 364 = 891, 529 + 317 = 846,
541 + 296 = 837, 541 + 386 = 927, 542 + 196 = 738,
542 + 376 = 918, 543 + 186 = 729, 543 + 276 = 819,
546 + 183 = 729, 546 + 192 = 738, 546 + 273 = 819,
546 + 291 = 837, 546 + 372 = 918, 546 + 381 = 927,
564 + 219 = 783, 564 + 327 = 891, 567 + 324 = 891,
569 + 214 = 783, 571 + 293 = 864, 572 + 346 = 918,
573 + 246 = 819, 573 + 291 = 864, 576 + 243 = 819,
576 + 342 = 918, 581 + 346 = 927, 583 + 146 = 729,
586 + 143 = 729, 586 + 341 = 927, 591 + 246 = 837,
591 + 273 = 864, 592 + 146 = 738, 593 + 271 = 864,
596 + 142 = 738, 596 + 241 = 837, 614 + 259 = 873,
614 + 358 = 972, 617 + 328 = 945, 618 + 327 = 945,
618 + 354 = 972, 619 + 254 = 873, 624 + 159 = 783,
624 + 357 = 981, 627 + 318 = 945, 627 + 354 = 981,
628 + 317 = 945, 629 + 154 = 783, 634 + 158 = 792,
634 + 257 = 891, 637 + 254 = 891, 638 + 154 = 792,
642 + 195 = 837, 643 + 275 = 918, 645 + 192 = 837,
645 + 273 = 918, 654 + 129 = 783, 654 + 138 = 792,
654 + 219 = 873, 654 + 237 = 891, 654 + 318 = 972,
654 + 327 = 981, 657 + 234 = 891, 657 + 324 = 981,
658 + 134 = 792, 658 + 314 = 972, 659 + 124 = 783,
659 + 214 = 873, 671 + 283 = 954, 673 + 245 = 918,
673 + 281 = 954, 675 + 243 = 918, 681 + 273 = 954,
683 + 271 = 954, 692 + 145 = 837, 695 + 142 = 837,
715 + 248 = 963, 716 + 238 = 954, 718 + 236 = 954,
718 + 245 = 963, 725 + 139 = 864, 729 + 135 = 864,
735 + 129 = 864, 735 + 246 = 981, 736 + 218 = 954,
736 + 245 = 981, 738 + 216 = 954, 739 + 125 = 864,
745 + 218 = 963, 745 + 236 = 981, 746 + 235 = 981,
748 + 215 = 963, 752 + 184 = 936, 754 + 182 = 936,
762 + 183 = 945, 763 + 182 = 945, 782 + 154 = 936,
782 + 163 = 945, 783 + 162 = 945, 784 + 152 = 936
Edit: well that was a mess. Hopefully this will look neater
2006-10-28 00:58:12 · answer #2 · answered by Pascal 7 · 1⤊ 0⤋
235+746=981 should do the trick. As a matter of fact, addition is communtative so the number of combinations is a good deal less.
I arrived to the answer by trying a few combinations, starting with 123+456=569. A little figuring can soon tell that 9 must be on the top and I simply tweaked the first to include 8.
2006-10-28 00:41:24 · answer #3 · answered by John H 4 · 2⤊ 0⤋
159 + 327 = 486
2006-10-28 00:50:23 · answer #4 · answered by newcamper 2 · 0⤊ 0⤋
wow. , there are 9! combinations. that makes 362880 ways to try out to find the answer. i really have no idea where to start ! i;m guessing the bigger numbers go on the rhs ?
i;m watching this for an answer. good question tho .. haha
2006-10-28 00:33:38 · answer #5 · answered by Anonymous · 0⤊ 1⤋
I'm not sure this is possible without carrying. I've been working on it for an hour...
2006-10-28 01:26:18 · answer #6 · answered by wildstar_2 6 · 0⤊ 1⤋
with carrying
159 + 624 = 783
591 + 246 = 837
without carrying, i don't know how???
that's quite tough
2006-10-28 00:59:56 · answer #7 · answered by lazareh 2 · 0⤊ 1⤋