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## A Mathematics Lesson Starter Of The Day

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• 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 3.2 out of 5 based on 164 votes.

Previous Day | This starter is for 2 July | Next Day

 124 + 659 = 783125 + 739 = 864127 + 359 = 486127 + 368 = 495128 + 367 = 495128 + 439 = 567129 + 357 = 486129 + 438 = 567129 + 654 = 783129 + 735 = 864134 + 658 = 792135 + 729 = 864138 + 429 = 567138 + 654 = 792139 + 428 = 567139 + 725 = 864142 + 596 = 738142 + 695 = 837143 + 586 = 729145 + 692 = 837146 + 583 = 729146 + 592 = 738152 + 487 = 639152 + 784 = 936154 + 629 = 783154 + 638 = 792154 + 782 = 936157 + 329 = 486157 + 482 = 639158 + 634 = 792159 + 327 = 486159 + 624 = 783162 + 387 = 549162 + 783 = 945163 + 782 = 945167 + 328 = 495167 + 382 = 549168 + 327 = 495173 + 286 = 459173 + 295 = 468175 + 293 = 468176 + 283 = 459182 + 367 = 549182 + 394 = 576182 + 457 = 639182 + 493 = 675182 + 754 = 936182 + 763 = 945183 + 276 = 459183 + 492 = 675183 + 546 = 729183 + 762 = 945184 + 392 = 576184 + 752 = 936186 + 273 = 459186 + 543 = 729 187 + 362 = 549187 + 452 = 639192 + 384 = 576192 + 483 = 675192 + 546 = 738192 + 645 = 837193 + 275 = 468193 + 482 = 675194 + 382 = 576195 + 273 = 468195 + 642 = 837196 + 542 = 738214 + 569 = 783214 + 659 = 873215 + 478 = 693215 + 748 = 963216 + 378 = 594216 + 738 = 954218 + 349 = 567218 + 376 = 594218 + 439 = 657218 + 475 = 693218 + 736 = 954218 + 745 = 963219 + 348 = 567219 + 438 = 657219 + 564 = 783219 + 654 = 873234 + 657 = 891235 + 746 = 981236 + 718 = 954236 + 745 = 981237 + 654 = 891238 + 419 = 657238 + 716 = 954239 + 418 = 657241 + 596 = 837243 + 576 = 819243 + 675 = 918245 + 673 = 918245 + 718 = 963245 + 736 = 981246 + 573 = 819246 + 591 = 837246 + 735 = 981248 + 319 = 567248 + 715 = 963249 + 318 = 567251 + 397 = 648254 + 619 = 873254 + 637 = 891257 + 391 = 648257 + 634 = 891259 + 614 = 873264 + 519 = 783269 + 514 = 783 271 + 593 = 864271 + 683 = 954273 + 186 = 459273 + 195 = 468273 + 546 = 819273 + 591 = 864273 + 645 = 918273 + 681 = 954275 + 193 = 468275 + 418 = 693275 + 643 = 918276 + 183 = 459276 + 318 = 594276 + 543 = 819278 + 316 = 594278 + 415 = 693281 + 394 = 675281 + 673 = 954283 + 176 = 459283 + 671 = 954284 + 391 = 675286 + 173 = 459291 + 357 = 648291 + 384 = 675291 + 546 = 837291 + 573 = 864293 + 175 = 468293 + 571 = 864294 + 381 = 675295 + 173 = 468296 + 541 = 837297 + 351 = 648314 + 658 = 972316 + 278 = 594317 + 529 = 846317 + 628 = 945318 + 249 = 567318 + 276 = 594318 + 627 = 945318 + 654 = 972319 + 248 = 567319 + 527 = 846324 + 567 = 891324 + 657 = 981327 + 159 = 486327 + 168 = 495327 + 519 = 846327 + 564 = 891327 + 618 = 945327 + 654 = 981328 + 167 = 495328 + 617 = 945329 + 157 = 486329 + 517 = 846341 + 586 = 927342 + 576 = 918 346 + 572 = 918346 + 581 = 927348 + 219 = 567349 + 218 = 567351 + 297 = 648352 + 467 = 819354 + 618 = 972354 + 627 = 981357 + 129 = 486357 + 291 = 648357 + 462 = 819357 + 624 = 981358 + 614 = 972359 + 127 = 486362 + 187 = 549362 + 457 = 819364 + 527 = 891367 + 128 = 495367 + 182 = 549367 + 452 = 819367 + 524 = 891368 + 127 = 495372 + 546 = 918376 + 218 = 594376 + 542 = 918378 + 216 = 594381 + 294 = 675381 + 546 = 927382 + 167 = 549382 + 194 = 576384 + 192 = 576384 + 291 = 675386 + 541 = 927387 + 162 = 549391 + 257 = 648391 + 284 = 675392 + 184 = 576394 + 182 = 576394 + 281 = 675397 + 251 = 648415 + 278 = 693418 + 239 = 657418 + 275 = 693419 + 238 = 657428 + 139 = 567429 + 138 = 567438 + 129 = 567438 + 219 = 657439 + 128 = 567439 + 218 = 657452 + 187 = 639452 + 367 = 819457 + 182 = 639457 + 362 = 819462 + 357 = 819467 + 352 = 819 475 + 218 = 693478 + 215 = 693482 + 157 = 639482 + 193 = 675483 + 192 = 675487 + 152 = 639492 + 183 = 675493 + 182 = 675514 + 269 = 783517 + 329 = 846519 + 264 = 783519 + 327 = 846524 + 367 = 891527 + 319 = 846527 + 364 = 891529 + 317 = 846541 + 296 = 837541 + 386 = 927542 + 196 = 738542 + 376 = 918543 + 186 = 729543 + 276 = 819546 + 183 = 729546 + 192 = 738546 + 273 = 819546 + 291 = 837546 + 372 = 918546 + 381 = 927564 + 219 = 783564 + 327 = 891567 + 324 = 891569 + 214 = 783571 + 293 = 864572 + 346 = 918573 + 246 = 819573 + 291 = 864576 + 243 = 819576 + 342 = 918581 + 346 = 927583 + 146 = 729586 + 143 = 729586 + 341 = 927591 + 246 = 837591 + 273 = 864592 + 146 = 738593 + 271 = 864596 + 142 = 738596 + 241 = 837614 + 259 = 873614 + 358 = 972617 + 328 = 945618 + 327 = 945618 + 354 = 972619 + 254 = 873624 + 159 = 783624 + 357 = 981 627 + 318 = 945627 + 354 = 981628 + 317 = 945629 + 154 = 783634 + 158 = 792634 + 257 = 891637 + 254 = 891638 + 154 = 792642 + 195 = 837643 + 275 = 918645 + 192 = 837645 + 273 = 918654 + 129 = 783654 + 138 = 792654 + 219 = 873654 + 237 = 891654 + 318 = 972654 + 327 = 981657 + 234 = 891657 + 324 = 981658 + 134 = 792658 + 314 = 972659 + 124 = 783659 + 214 = 873671 + 283 = 954673 + 245 = 918673 + 281 = 954675 + 243 = 918681 + 273 = 954683 + 271 = 954692 + 145 = 837695 + 142 = 837715 + 248 = 963716 + 238 = 954718 + 236 = 954718 + 245 = 963725 + 139 = 864729 + 135 = 864735 + 129 = 864735 + 246 = 981736 + 218 = 954736 + 245 = 981738 + 216 = 954739 + 125 = 864745 + 218 = 963745 + 236 = 981746 + 235 = 981748 + 215 = 963752 + 184 = 936754 + 182 = 936762 + 183 = 945763 + 182 = 945782 + 154 = 936782 + 163 = 945783 + 162 = 945784 + 152 = 936

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## GCSE Revision and Practice

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 Teacher, do your students have access to computers?Do they have iPads or Laptops in Lessons? Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Here a concise URL for a version of this page without the comments.

Transum.org/go/?Start=July2

Here is the URL which will take them to an interactive pupil version of this puzzle.

Transum.org/go/?to=ninedigits

For Students:

For All: