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 Pythagorean Chain (Posted on 2006-03-20)
Take a right triangle with integer sides A, B, & C.
(C need not be the hypotenuse.)

To side C attach another right triangle with integer sides C, D & E.

On this new triangle attach another right triangle to either side D or E. Continue the process of attaching a new right triangle to the previous; creating a chain of right triangles.

Three further rules:
1. No side length may be repeated.
2. No triangles may overlap.
3. No side may have length over 10000.

How many triangles can you make in this chain?

 See The Solution Submitted by Jer Rating: 3.5000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Is 10000 too big? | Comment 16 of 18 |
(In reply to Is 10000 too big? by Jer)

With a limit of 1000, the program does not crash (as the chain doesn't get long enough to generate a large enough number of recursions), but still does not have time to explore all the possibilities.  This is the best it came up with in the time alloted to it:

` 1                3-    4-    5 2                5-   12-   13 3               12-   16-   20 4               16-   30-   34 5               30-   40-   50 6               40-   42-   58 7               42-   56-   70 8               56-   90-  106 9               90-  120-  150 10             120-  126-  174 11             126-  168-  210 12             168-  224-  280 13             224-  360-  424 14             360-  378-  522 15             378-  504-  630 16             504-  550-  746 17             480-  550-  730 18             480-  640-  800 19             640-  672-  928 20             104-  672-  680 21             104-  153-  185 22             153-  204-  255 23             204-  253-  325 24             325-  780-  845 25             112-  780-  788 26             112-  180-  212 27             180-  189-  261 28             189-  252-  315 29             252-  275-  373 30             275-  660-  715 31             660-  693-  957 32             140-  693-  707 33             140-  147-  203 34             147-  196-  245 35             245-  588-  637 36             588-  784-  980 37             105-  784-  791 38             105-  208-  233 39             208-  306-  370 40             306-  408-  510 41             408-  506-  650 42             650-  720-  970 43              76-  720-  724 44              76-  357-  365 45             357-  476-  595 46             476-  765-  901 47              96-  765-  771 48              96-  110-  146 49             110-  264-  286 50             264-  352-  440 51             352-  420-  548 52             420-  441-  609 53             200-  609-  641 54             200-  375-  425 55             375-  500-  625 56             500-  525-  725 57             525-  700-  875 58             240-  700-  740 59             240-  320-  400 60             320-  336-  464 61             336-  377-  505 62             145-  348-  377 63             348-  805-  877 64             276-  805-  851 65             276-  368-  460 66             368-  465-  593 67             465-  620-  775 68             620-  651-  899 69             260-  651-  701 70             260-  288-  388 71             288-  330-  438 72             330-  792-  858 73              69-  792-  795 74             477-  636-  795 75             265-  636-  689 76             364-  585-  689 77             585-  648-  873 78             270-  648-  702 79             270-  704-  754 80             528-  704-  880 81              46-  528-  530 82             192-  494-  530 83             192-  220-  292 84             220-  231-  319 85             231-  308-  385 86             308-  435-  533 87             533-  756-  925 88             345-  756-  831 89             345-  828-  897 90             205-  828-  853 91              84-  187-  205 92              84-  135-  159 93             135-  324-  351 94             324-  432-  540 95             432-  495-  657 96             495-  840-  975 97             130-  840-  850 98             130-  144-  194 99             144-  165-  219 100            165-  396-  429 101            396-  403-  565 102            155-  372-  403 103            155-  468-  493 104            195-  468-  507 105            195-  216-  291 106            216-  405-  459 107            312-  459-  555 108            312-  416-  520 109            520-  576-  776 110             68-  576-  580 111             68-  285-  293 112            285-  380-  475 113            380-  399-  551 114            399-  532-  665 115            532-  624-  820 116            492-  656-  820 117            369-  492-  615 118            615-  728-  953 119            546-  728-  910 120            272-  546-  610 121            225-  272-  353 122            225-  924-  951 123            143-  924-  935 124             55-  132-  143 125             48-   55-   73 126             48-  575-  577 127            161-  552-  575 128            552-  736-  920 129            273-  736-  785 130            136-  273-  305 131            102-  136-  170 132             72-  154-  170 133             65-   72-   97 134             65-  156-  169 135            156-  455-  481 136            481-  600-  769 137            450-  600-  750 138            450-  544-  706 139             33-  544-  545 140            184-  513-  545 141            513-  684-  855 142            456-  855-  969 143            456-  608-  760 144            570-  760-  950 145            266-  912-  950 146            215-  912-  937 147            215-  516-  559 148            387-  516-  645 149            387-  884-  965 150            340-  816-  884 151            160-  300-  340 152             36-  160-  164 153             15-   36-   39 154              8-   15-   17 155              6-    8-   10 156             10-   24-   26 157             24-   45-   51 158             45-  108-  117 159             44-  117-  125 160             75-  100-  125 161             75-  936-  939 162            310-  936-  986 163            310-  744-  806 164            558-  744-  930`

 Posted by Charlie on 2006-03-21 10:47:38

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