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 Four generations (Posted on 2020-07-06)
Let S be a set of all six-digit integers.

Let S1 be a subset of S, including all members of S such that each consists
of distinct digits.
Let S2 be a subset of S1, including all members of S1 each with 5 being the difference between its largest digit and its lowest one.
Let S3 be a subset of S2, comprising all elements of S2 divisible by 143.

What is the cardinality of S3 ?

Explain your way of reasoning.

 No Solution Yet Submitted by Ady TZIDON Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: part 1 via computer | Comment 3 of 9 |
(In reply to part 1 via computer by Steven Lord)

This is wrong; I neglected to check for "distinct" digits.

There are some:

101530 102245 102531 103532 104533 105105 105534 110253 111540 113256 115401 116116 116545 121264 121550 122265 123266 126126 126412 126555 132561 133562 134563 135564 136136 136422 136565 145002 146146 146432 150150 153010 154011 154440 155012 156156 156442 161161 162162 163163 164164 165165 165451 166166 166452 202345 205205 210353 212641 213356 213642 214500 214643 215501 215644 216216 216645 221364 222651 224367 224510 226512 227227 227656 232375 232661 233376 234377 234520 237237 237523 237666 243672 244530 244673 245102 245674 246675 247247 247533 247676 250250 253110 254540 256113 257257 257543 261261 264121 265122 265551 266123 267267 267553 272272 273273 274274 275275 276276 276562 277277 277563 301015 302445 305305 310453 311025 313456 316316 321035 321464 323752 324467 324753 325611 325754 326612 326755 327327 327756 331045 332475 333762 335478 335621 337623 338338 338767 340054 341055 343486 343772 344487 345202 345488 345631 348348 348634 348777 350350 353210 354783 355641 355784 356213 356785 357786 358358 358644 358787 361361 364221 365651 367224 368368 368654 372372 375232 376233 376662 377234 378378 378664 383383 384384 385385 386386 387387 387673 388388 388674 400543 401115 401544 402545 405405 410553 412126 413556 416416 421564 422136 424567 427427 432146 432575 434005 434863 435578 435864 436722 436865 437723 437866 438438 438867 440154 442156 443586 444015 444873 445302 446589 446732 448734 449449 449878 450021 450450 451022 451165 452023 452166 453024 453310 454025 454597 454883 455598 456313 456599 456742 459459 459745 459888 461461 464321 465894 466752 466895 467324 467896 468897 469469 469755 469898 472472 475332 476762 478335 479479 479765 483483 486343 487344 487773 488345 489489 489775 494494 495495 496496 497497 498498 498784 499499 499785 500214 500500 501215 501501 502502 503503 504504 505505 510224 510510 511654 512226 512655 513656 516516 520234 520520 521664 523237 524667 527527 530101 530244 530530 531102 532103 532675 533104 533247 534105 535678 538538 540111 540254 540540 543257 543400 543686 544401 545116 545402 545974 546689 546975 547833 547976 548834 548977 549549 549978 550121 550550 551265 553267 553410 554697 555126 555984 556413 557843 559845 561132 561561 562133 562276 563134 563277 564135 564421 565136 565994 567424 567853 572572 575432 577863 578435 583583 586443 587873 589446 594594 597454 598455 598884 599456 611325 611611 612326 612612 613613 614614 615615 616616 621335 621621 622765 623337 623766 624767 627627 631345 631631 632775 634348 635778 638638 641212 641355 641641 642213 643214 643786 644215 644358 645216 646789 649649 651222 651365 651651 654368 654511 654797 655512 656227 656513 658944 659945 661232 661661 662376 664378 664521 666237 667524 668954 672243 672672 673244 673387 674245 674388 675246 675532 676247 678535 678964 683683 686543 688974 689546 694694 697554 698984 722436 722722 723437 723723 724724 725725 726726 727727 732446 732732 733876 734448 734877 735878 738738 742456 742742 743886 745459 746889 749749 752323 752466 752752 753324 754325 754897 755326 755469 756327 762333 762476 762762 765479 765622 766623 767338 767624 772343 772772 773487 775489 775632 777348 778635 783354 783783 784355 784498 785356 785499 786357 786643 787358 789646 794794 797654 833547 833833 834548 834834 835835 836836 837837 838838 843557 843843 844987 845559 845988 846989 849849 853567 853853 854997 863434 863577 863863 864435 865436 866437 867438 873444 873587 873873 876733 877734 878449 878735 883454 883883 884598 886743 888459 889746 894465 894894 895466 896467 897468 897754 898469 944658 944944 945659 945945 946946 947947 948948 949949 954668 954954 964678 964964 974545 974688 974974 975546 976547 977548 978549 984555 984698 984984 987844 988845 989846 994565 994994 997854

Edited on July 6, 2020, 10:32 am
 Posted by Charlie on 2020-07-06 10:22:55

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