Nine Digit Sum  - A Maths Starter Of The Day

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A Mathematics Lesson Starter Of The Day

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Topics: Starter | Arithmetic | Place Value | Problem Solving | Puzzles

  • Transum,
  • Wednesday, July 5, 2017
  • What strategy could you use to solve a puzzle like this? I began by calculating the sum of the digits one to nine. I then considered in turn the following three possibilities:

    1. The sum of each column is less than ten which means there is no ‘carry’;
    2. There is one carry (either from the units to the tens or the tens to the hundreds column);
    3. There are two carries (both from the units to the tens and the tens to the hundreds column).

    The rest of the strategy and all 336 different solutions are given in the answer section below for subscribers.

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This starter has scored a mean of 2.7 out of 5 based on 27 votes.


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Answers

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


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