## Rubik Distance

The name probably originates with the player Rubik87; perhaps he was the first to identify and explain the concept.

The idea is to express the ‘reach’ of a given piece – how much distance it can cover, combining both horizontal and vertical dimensions.

A quasi-mathematical definition is:

The sum of the dimensions of the rectangle which encompasses two most distant squares of the piece.

For many pieces, it is simply the entire piece.

I5 travels 5 squares in one direction and one in the other for a total of 5+1 = 6.

Similarly, L5 and N are 4+2 = 6, and V, W, and Z are 3+3 = 6.

Six is the maximum.

L4 and Z4 are 3+2 = 5.

They are sub-pieces of F, T, P, and U which are also 5’s.

I4 = 4+1 is a 5, as is Y.

Y can derive its 5-ness from either the I4 subpiece (the long bit) or an embedded L4, using the knob.

For the remaining pieces, it works similarly, but with their smaller values of less than 5, there is less importance.

### Application

The main use of Rubik Distance comes in the opening moves, or sometimes later in the game, when a delayed connection is made.

Since the entire board is 20×20, in order for blue pieces to meet, or connect with, red pieces (on move 4 for blue), the total of the first four blue and first 3 red must be 41 (or more).

Since 7 fives won’t do that, you need some sixes. In fact among the first 6 moves (3 from each color), there can be at most one five. That makes the total for those 6 moves 5 x 6 + (5 or 6) = 35 or 36, at which point a five or six will make the connection.

If there are 2 fives in the first 6 moves, it falls short, since 4 x 6 + 2 x 5 = 34, and no piece has Rubik distance 7.

For more on Rubik Distance, see the post: Early Pieces, Rubik Length, and True Length, here:

Pingback: Early Pieces, Rubik Length and True Length | Blokus Strategy