A lost treasure (Series within Parallel resistor combinations.)

G'day G'day Folks,

At one time I wrote test questions for electrical students. To ensure
consistency in marking I resolved to have integer answers to avoid
issues arising from early rounding.

Here is a question I posted many years ago on sci.math.

Connecting R1 and R2 in series gives a total resistance of R1 + R2
Connecting R3 and R4 in series gives a total resistance of R3 + R4
Putting these series combination in parallel gives a combined
resistance of (R1 + R2)(R3 + R4)/(R1 + R2 + R3 + R4) = Rx (say)
If I connect the node between R1 & R2 to the node between R3 & R4
the circuit is transformed to a parallel within series connection.
The resistance is now Ry = (R1 x R3)/(R1 + R3) + (R2 x R4)/(R2 + R4)
The maths challenge this time is that I'd like, R1, R2, R3, R4, Rx,
and Ry to all be positive integers, preferably under 100.

I obtained an incredible answer from someone, most probably ksbrown in
which it was pointed out the advisability of adding some further
conditions

1. The solutions when the nodes were connected and left unconnected
should be different ie R1 x R4 should not equal R2 x R3.

2. Not only should Rx and Ry be integers but so should their
components. (R1R3)/(R1+R3) and (R2R4)/(R2+R4)

What I'd like is a table containing perhaps a dozen solutions.

I'd be quite happy if someone produced the answers using a brute force
computer method. While pure mathematical methods are more elegant I'm
no longer sure I could follow them.

Best wishes,
--
Quentin Grady ^ ^ /
New Zealand, >#,#< [
/ \ /\
"... and the blind dog was leading."

http://homepages.paradise.net.nz/quentin
.

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