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Re: Crossed Ladders Problem (again)
Posted:
Aug 24, 2001 7:01 AM
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> I wonder what the simplest rational solution is?
Well, the simplest is for the width = 8, the first ladder = 17, the second
ladder = 10, and the height is 30/7. However I decided to use GP-Pari to
find integer solutions to this, which it did quickly -
Here they are for all widths from 1 to 10,000:
Double Ladders Problem - Integer Solutions
------------------------------ + ------------------------------
sorted by width | sorted by height
------------------------------ | ------------------------------
width A B height | width A B height
------------------------------ | ------------------------------
56 119 70 30 | 56 119 70 30
105 273 175 90 | 140 364 175 80
117 533 195 120 | 105 273 175 90
140 364 175 80 | 117 533 195 120
165 915 429 275 | 300 500 375 144
224 1799 476 340 | 364 1300 455 224
260 1700 676 455 | 400 1625 500 252
300 500 375 144 | 165 915 429 275
364 1300 455 224 | 528 1628 660 315
400 1625 500 252 | 224 1799 476 340
462 2562 770 495 | 260 1700 676 455
495 3729 825 560 | 672 4728 840 455
496 2015 1054 630 | 462 2562 770 495
525 1875 875 504 | 760 3838 950 495
528 1628 660 315 | 525 1875 875 504
552 1702 1173 630 | 495 3729 825 560
555 4181 1443 1008 | 612 1887 1020 560
595 2125 1547 840 | 496 2015 1054 630
612 1887 1020 560 | 552 1702 1173 630
616 4334 1309 910 | 992 7967 1240 680
651 6851 1085 770 | 651 6851 1085 770
672 4728 840 455 | 760 1976 1615 800
675 9125 1125 819 | 675 9125 1125 819
741 4845 1235 819 | 741 4845 1235 819
760 1976 1615 800 | 595 2125 1547 840
760 3838 950 495 | 616 4334 1309 910
775 9703 2015 1560 | 555 4181 1443 1008
819 15981 3731 2964 | 1848 3927 3080 1440
931 22819 3325 2800 | 775 9703 2015 1560
980 4949 2548 1584 | 980 4949 2548 1584
992 7967 1240 680 | 1015 17777 2639 2142
1015 17777 2639 2142 | 1848 6600 3927 2240
1463 8113 5225 3080 | 3864 23345 4830 2574
1533 16133 5475 3960 | 4004 22204 5005 2640
1547 92053 5525 5015 | 931 22819 3325 2800
1848 3927 3080 1440 | 819 15981 3731 2964
1848 6600 3927 2240 | 1463 8113 5225 3080
1908 8692 5883 3360 | 1908 8692 5883 3360
1953 8897 6975 3780 | 1953 8897 6975 3780
2135 37393 7625 6120 | 2256 9165 6956 3780
2200 22055 5720 4256 | 3015 67871 5025 3795
2256 9165 6956 3780 | 1533 16133 5475 3960
2275 14875 8125 5096 | 5720 57343 7150 3990
2464 54236 5236 4257 | 2200 22055 5720 4256
2465 35785 6409 5075 | 2464 54236 5236 4257
2716 19109 9700 6240 | 6732 30668 8415 4320
2717 25883 15067 9405 | 6500 42500 8125 4368
2961 31161 13489 9240 | 4200 25375 7000 4576
3015 22713 13735 8400 | 3640 18382 7735 4950
3015 67871 5025 3795 | 1547 92053 5525 5015
3096 55771 9546 7770 | 2465 35785 6409 5075
3150 70910 8190 6831 | 2275 14875 8125 5096
3267 44165 14883 10920 | 4389 41811 7315 5130
3465 15785 9009 5400 | 3784 20984 8041 5280
3496 33304 7429 5472 | 7568 83420 9460 5313
3619 139355 20069 17290 | 3465 15785 9009 5400
3640 18382 7735 4950 | 7616 121975 9520 5456
3780 39780 11655 8624 | 3496 33304 7429 5472
3784 20984 8041 5280 | 4851 80115 8085 5984
3864 23345 4830 2574 | 2135 37393 7625 6120
4004 22204 5005 2640 | 2716 19109 9700 6240
4025 46375 14375 10626 | 4512 27260 9588 6435
4064 32639 16510 10710 | 9112 155038 11390 6545
4095 133119 10647 9152 | 3150 70910 8190 6831
4200 25375 7000 4576 | 6375 54375 10625 7344
4240 42506 17225 11970 | 3096 55771 9546 7770
4389 41811 7315 5130 | 3015 22713 13735 8400
4465 42535 11609 8550 | 4465 42535 11609 8550
4505 191489 11713 10234 | 3780 39780 11655 8624
4512 27260 9588 6435 | 6552 29848 13923 8640
4851 26901 22099 11880 | 7482 108618 12470 9135
4851 80115 8085 5984 | 4095 133119 10647 9152
5075 63539 18125 13650 | 2961 31161 13489 9240
5112 30885 15762 10010 | 2717 25883 15067 9405
5236 36839 29036 16016 | 7917 154483 13195 9880
5340 40228 16465 11200 | 6320 63358 13430 9975
5720 57343 7150 3990 | 5112 30885 15762 10010
5863 120263 32513 25256 | 4505 191489 11713 10234
5973 98645 33123 24480 | 6384 76741 13566 10350
6061 87989 57739 34713 | 4025 46375 14375 10626
6320 31916 25675 13860 | 4064 32639 16510 10710
6320 63358 13430 9975 | 3267 44165 14883 10920
6375 54375 10625 7344 | 8721 222471 14535 11050
6384 76741 13566 10350 | 5340 40228 16465 11200
6500 42500 8125 4368 | 4851 26901 22099 11880
6545 55825 17017 12240 | 4240 42506 17225 11970
6552 29848 13923 8640 | 6545 55825 17017 12240
6732 30668 8415 4320 | 7752 131898 16473 13090
6732 333268 37332 33075 | 8128 130175 17272 13640
6864 82511 21164 16100 | 5075 63539 18125 13650
7021 59885 25075 17136 | 6320 31916 25675 13860
7371 298571 33579 29520 | 5236 36839 29036 16016
7392 59367 40992 23936 | 6864 82511 21164 16100
7400 370037 37370 33330 | 7535 207281 19591 16632
7482 108618 12470 9135 | 7021 59885 25075 17136
7535 207281 19591 16632 | 3619 139355 20069 17290
7568 83420 9460 5313 | 7392 59367 40992 23936
7616 121975 9520 5456 | 5973 98645 33123 24480
7752 131898 16473 13090 | 5863 120263 32513 25256
7917 154483 13195 9880 | 7960 79799 40198 26334
7960 79799 40198 26334 | 7371 298571 33579 29520
8128 130175 17272 13640 | 8487 174087 38663 30996
8305 228463 46055 37800 | 9344 299081 37960 32760
8487 174087 38663 30996 | 6732 333268 37332 33075
8721 222471 14535 11050 | 7400 370037 37370 33330
9112 155038 11390 6545 | 6061 87989 57739 34713
9344 299081 37960 32760 | 8305 228463 46055 37800
9744 272919 68556 54340 | 9867 192533 64515 47880
9867 192533 64515 47880 | 9744 272919 68556 54340
- Randall
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