Resistor grid puzzle

Imagine a rectangular grid of 1 ohm resistors, 3 on a side like this:

  A   ___     ___     ___
   |-|___|-|-|___|-|-|___|-|
  .-.     .-.     .-.     .-.
  | |     | |     | |     | |
  | |     | |     | |     | |
  '-' ___ '-' ___ '-' ___ '-'
   |-|___|-|-|___|-|-|___|-|
  .-.     .-.     .-.     .-.
  | |     | |     | |     | |
  | |     | |     | |     | |
  '-' ___ '-' ___ '-' ___ '-'
   |-|___|-|-|___|-|-|___|-|
  .-.     .-.     .-.     .-.
  | |     | |     | |     | |
  | |     | |     | |     | |
  '-' ___ '-' ___ '-' ___ '-'
   |-|___|-|-|___|-|-|___|-|
                            B


Now expand the grid so it's 20 resistors on a side.  What is the
resistance
between diagonally opposite corners A and B?

Does anyone see a shortcut method?