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## A Mathematics Lesson Starter Of The Day

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• Transum,
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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 171 votes.

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 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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## Hello World

You are buying a (driverless) car. One vehicle is programmed to save as many lives as possible in a collision. Another promises to prioritize the lives of its passengers. Which do you choose?

Welcome to the age of the algorithm, the story of a not-too-distant future where machines rule supreme, making important decisions – in healthcare, transport, finance, security, what we watch, where we go even who we send to prison. So how much should we rely on them? What kind of future do we want?

Hannah Fry takes us on a tour of the good, the bad and the downright ugly of the algorithms that surround us. In Hello World she lifts the lid on their inner workings, demonstrates their power, exposes their limitations, and examines whether they really are an improvement on the humans they are replacing. more...

 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).

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:

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