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Pythagorean Chain (Posted on 2006-03-20) Difficulty: 3 of 5
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.)
Some Thoughts 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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