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Pythagorean areas (Posted on 2017-11-17) Difficulty: 3 of 5
List all Pythagorean triangles whose area utilizes
9 different digits.

See The Solution Submitted by Ady TZIDON    
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Solution computer solution after fixing bug | Comment 6 of 7 |
My bug had been the result of having N as being declared local as well as a parameter in fnFactor, something added during debugging but should have been removed. That bug having been found and the confusion between global and local variables (as parameters are local by default), the program took a few hours to run, under DOSBox.  

There are 429 such pythagorean triangles, where the area repeats none of the 9 digits it uses.  I've used a second program to clean up the output: aligning in columns and eliminating any case that merely duplicates the preceding one with the two legs reversed. What's left after that removal of duplicates is the 429-member list, sorted on hypotenuse:

      a      b   hypotenuse  

13692 18256 22820 18372 13779 22965 18252 14560 23348 15631 17640 23569 16300 17115 23635 19188 14391 23985 20706 12320 24094 20502 13936 24790 18837 17284 25565 20572 15429 25715 15624 20832 26040 22230 13832 26182 22487 13416 26185 16128 21504 26880 21596 16197 26995 16206 21608 27010 21930 16128 27222 22484 15387 27245 12236 24477 27365 17980 20661 27389 25102 11736 27710 13680 24192 27792 23919 14508 27975 14014 24552 28270 23779 15372 28315 16992 22656 28320 17106 22808 28510 15876 23843 28645 11960 26208 28808 25440 13568 28832 21924 18768 28860 11105 26652 28873 27144 10208 29000 23532 17649 29415 26280 13216 29416 20475 21172 29453 18066 24088 30110 23782 18480 30118 9780 28525 30155 25092 17056 30340 26880 14336 30464 26845 14664 30589 22176 21120 30624 17136 25623 30825 22165 21780 31075 21620 22701 31349 29309 12012 31675 23058 21960 31842 12441 29412 31935 24252 20961 32055 19720 25536 32264 19434 25912 32390 30525 12276 32901 32067 8144 33085 28480 17679 33521 25896 21472 33640 27012 20259 33765 20472 27296 34120 26796 21285 34221 9639 33048 34425 25806 22792 34430 20658 27544 34430 33660 8775 34785 33733 8820 34867 15288 31360 34888 13535 32484 35191 33660 10608 35292 15738 31640 35338 33696 12672 36000 28884 21663 36105 31935 17032 36193 34099 12168 36205 30566 19488 36250 26292 25040 36308 35100 9315 36315 23088 28341 36555 14125 33900 36725 17621 32340 36829 18744 31808 36920 16898 33264 37310 35574 14432 38390 18718 34080 38882 36960 12672 39072 32868 21165 39093 35970 15344 39106 36738 13816 39250 26390 29232 39382 36225 15660 39465 21060 33408 39492 31518 24024 39630 33330 21528 39678 33948 20736 39780 37835 12972 39997 29949 26568 40035 32148 24111 40185 8207 39624 40465 38962 11280 40562 38430 13176 40626 29172 28305 40647 40095 8100 40905 12213 39100 40963 28122 30096 41190 26367 31680 41217 38194 15792 41330 18260 38097 42247 8930 41496 42446 36540 22736 43036 22923 36764 43325 11900 41667 43333 10255 42312 43537 42745 9300 43745 13156 41745 43769 43483 5544 43835 38372 21525 43997 7560 43776 44424 29375 33540 44585 9801 43560 44649 39585 21112 44863 17260 41424 44876 18759 40788 44895 36060 27045 45075 34960 28497 45103 39960 21312 45288 44583 8056 45305 8127 44936 45665 38129 25140 45671 36564 27423 45705 31005 34344 46269 43820 15024 46324 44982 11424 46410 6020 46029 46421 23661 40152 46605 46189 7752 46835 28134 37512 46890 29667 36344 46915 28224 37632 47040 18125 43500 47125 18140 43536 47164 24024 40768 47320 12852 45936 47700 43860 18832 47732 45567 14256 47745 28668 38224 47780 7345 47460 48025 47804 5328 48100 38748 29061 48435 5280 48256 48544 13629 46728 48675 22575 43164 48711 47671 11880 49129 47874 11880 49326 39596 29697 49495 25520 42891 49909 13575 48204 50079 46683 18144 50085 10266 49088 50150 22940 45312 50788 19540 46896 50804 49140 12896 50804 44910 23952 50898 48222 17296 51230 30924 41232 51540 44330 26832 51818 37548 35760 51852 9988 51045 52013 7969 51492 52105 41892 31419 52365 8021 51828 52445 29140 43632 52468 28495 44100 52505 51408 10944 52560 47124 24157 52955 50197 18060 53347 52972 9975 53903 46207 28224 54145 32538 43384 54230 20885 50124 54301 36890 39864 54314 37761 39560 54689 54416 8937 55145 12141 53960 55309 41944 36192 55400 52460 18375 55585 50358 23544 55590 18174 52768 55810 10788 55216 56260 44022 35496 56550 28776 48832 56680 27258 49880 56842 54036 17952 56940 56303 8580 56953 5418 56760 57018 45756 34317 57195 56420 9975 57295 57456 5760 57744 34758 46344 57930 32100 48685 58315 24544 52992 58400 35172 46896 58620 44958 37944 58830 51240 29216 58984 47356 35517 59195 55458 20856 59250 58487 9816 59305 47596 35697 59495 27775 52668 59543 7920 59136 59664 12740 58464 59836 58807 13176 60265 36186 48248 60310 54351 27360 60849 42220 44331 61219 59752 13920 61352 8827 60840 61477 4335 61336 61489 29302 54264 61670 8468 61101 61685 54615 29128 61897 61488 8235 62037 53922 30960 62178 45192 43040 62408 55883 28044 62525 43300 45465 62785 57615 25384 62959 32383 54060 63017 26220 57456 63156 62279 11160 63271 24390 58536 63414 60368 19551 63455 7446 63072 63510 38256 51008 63760 8073 64020 64527 55419 33592 64805 17205 62496 64821 58007 30324 65455 7168 65340 65732 27840 60003 66147 62580 21456 66156 19890 63504 66546 62361 23452 66625 59780 29415 66625 33500 58011 66989 14443 65520 67093 62488 24480 67112 8806 66792 67370 63531 23892 67875 67893 9576 68565 19257 66024 68775 29975 61908 68783 26645 63948 69277 69069 8208 69555 7334 69480 69866 66924 22165 70499 9390 70112 70738 12236 69825 70889 70308 10881 71145 7163 70884 71245 27620 66288 71812 71383 7956 71825 4169 71760 71881 4356 71808 71940 67818 24624 72150 20258 69456 72350 27875 66900 72475 72688 3795 72787 72114 11880 73086 16074 71440 73226 4641 73188 73335 20559 70488 73425 16383 71656 73505 13255 72300 73505 26767 68544 73585 28510 68424 74126 73143 18576 75465 73206 20440 76006 12059 75180 76141 76125 11340 76965 14467 75756 77125 15045 75992 77467 4464 77777 77905 76555 15012 78013 73885 25332 78107 76041 19312 78455 76293 19376 78715 6749 78660 78949 25824 75320 79624 10292 79431 80095 25980 75775 80105 11020 79515 80275 78155 20868 80893 79596 16415 81271 80475 11988 81363 78939 20048 81445 11732 81705 82543 78982 24240 82618 82500 10575 83175 83205 3784 83291 18324 81440 83476 83420 8589 83861 12831 82908 83895 82175 22836 85289 17860 83895 85775 15477 84420 85827 83385 20952 85977 3666 86112 86190 2919 86920 86969 88396 5565 88571 18352 86655 88577 86436 21952 89180 7910 89208 89558 9614 91080 91586 91080 13696 92104 18145 90300 92105 15876 91168 92540 14620 91872 93028 92781 7392 93075 91482 18920 93418 15947 92196 93565 20930 91392 93758 21217 92544 94945 4429 95172 95275 96152 15840 97448 97767 12920 98617 97185 17528 98753 97552 17589 99125 99081 7560 99369 98741 13860 99709 99710 9672 100178 13410 100128 101022 17110 100224 101674 101556 7533 101835 10373 101436 101965 6795 102492 102717 101885 16188 103163 18623 101580 103273 103740 4464 103836 103103 17304 104545 10982 104040 104618 8060 104625 104935 6188 105105 105287 14980 104325 105395 105006 15840 106194 107226 9768 107670 107712 3315 107763 8873 108864 109225 11340 109056 109644 12606 109080 109806 13902 109120 110002 17874 108832 110290 14260 110055 110975 11580 111447 112047 10668 111760 112268 13362 113184 113970 13617 115344 116145 4982 117024 117130 118560 15616 119584 119756 8883 120085 120900 4743 120993 16140 120512 121588 123310 8664 123614 6090 123552 123702 2057 124440 124457 2185 125628 125647 127260 4944 127356 127908 7315 128117 129456 6617 129625 129479 7920 129721 3619 133620 133669 7770 135864 136086 137532 9999 137895 2299 139080 139099 12430 140184 140734 2665 142032 142057 10165 142932 143293 3942 143856 143910 2652 146511 146535 4905 148472 148553 9534 154440 154734 156426 10440 156774 10817 156660 157033 9295 156948 157223 4122 157296 157350 158670 7216 158834 6042 160056 160170 162855 7084 163009 10912 168960 169312 7238 170016 170170 171972 9835 172253 173020 4992 173092 176900 8925 177125 1482 183024 183030 183596 9072 183820 184404 8928 184620 4300 184875 184925 188895 9036 189111 2057 192324 192335 199892 5019 199955 1276 203520 203524 204967 8544 205145 7161 211840 211961 214140 7605 214275 3345 223768 223793 225742 6720 225842 248500 3525 248525 2145 255608 255617 261324 6507 261405 262086 1448 262090 6561 265680 265761 5529 268128 268185 6360 280864 280936 295668 3845 295693 315835 3372 315853 4355 379308 379333 387192 3520 387208 389360 4992 389392 2214 408480 408486 4393 419520 419543 2769 425960 425969 2292 437769 437775 470442 3880 470458 477477 2764 477485 979 479220 479221 484120 3936 484136 515108 3045 515117 2455 602700 602705 3128 611520 611528 2778 643104 643110 1335 891112 891113 1431 1023880 1023881

Edited on November 19, 2017, 9:45 am
  Posted by Charlie on 2017-11-19 08:44:36

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