Need help with series-parallel resitor networks
You add the conductances (reciprocal of resistance) and then convert back to resistance. For example, lets say we have 500, 1500, and 2500 ohm resistors in parallel. The total resistance is:

1 / ((1/500) + (1/1500) + (1/2500)) = 326.1 ohms.

For 2 resistors in parallel you can also use (R1 * R2) / (R1 + R2) e.g. for 500 and 700 ohms:

(500 * 700) / (500 + 700) = 291.7 ohms.

For your example of the 10, 20 and 30 ohms in a 3 x 3 network, you can either work out each row then add the results, or multiply each value by three and calculate directly:

    |
10 20 30 
10 20 30
10 20 30
    |


1 / ((1/30) + (1/60) + (1/90)) = 16.3636... ohms.

If the example is like this (in/out at top and bottom of matrix):

    |
10 10 10
20 20 20
30 30 30
    |


then the result is 20 ohms (row 1 is 3.33... row 2 is 6.66... row three is 10 - added together is 20) which agrees with the answer you have.