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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.)
No Subject | Comment 7 of 18 |

A computer program comes up with 12471 Pythagorean triples--too many to list here--starting with 3-4-5 and ending with 6000-8000-10000.

    3     4     5
    6     8    10
    5    12    13
    9    12    15
    8    15    17
   12    16    20
    7    24    25
   15    20    25
   10    24    26
   20    21    29
   18    24    30
   16    30    34
   21    28    35
   12    35    37
   15    36    39
   24    32    40
    9    40    41
   27    36    45
   14    48    50
...
 5988  7984  9980
 1269  9900  9981
 3417  9380  9983
 3840  9216  9984
 1575  9860  9985
 4656  8833  9985
 5991  7988  9985
 6943  7176  9985
 5890  8064  9986
 6237  7800  9987
 3078  9504  9990
 3240  9450  9990
 5616  8262  9990
 5994  7992  9990
 6695  7416  9991
 6392  7680  9992
 5997  7996  9995
 4704  8820  9996
 2772  9605  9997
 3845  9228  9997
 4795  8772  9997
 6253  7800  9997
 1980  9801  9999
 2800  9600 10000
 3520  9360 10000
 5376  8432 10000
 6000  8000 10000

Edited on March 20, 2006, 4:20 pm
  Posted by Charlie on 2006-03-20 16:15:15

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