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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)

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 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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