# Karl's Race

###
A Game on Karl Scherer's Alternating Tiling

by Ingo Althöfer, 2006

Latest Update, May 2015

A tiling of a big square by at least two smaller squares
is called **alternating**, when there are no two
neighboring squares of the same size.
In his nice book **"New Mosaics"**, published in 1997,
**Dr. Karl Scherer** claims
that the following example (designed by himself)
has minimum number (= 20) of small squares.

**Karl Scherer** presents another beautiful solution with 21 little
squares: here each side length from 1 to 5 occurs exactly
in four squares, and length 6 occurs once, in the center.

Seeing this 21-solution I fell in love with it immediately.
You can buy a nice wooden version in a web shop.
Unfortunately, at that place Karl Scherer is not mentioned
as the designer (although I mailed this information).
Shame on the shop man!

##
Karl's Race:

###
"EinStein würfelt nicht" without Numbers

"EinStein würfelt nicht" (Ewn) is my bestknown 2-person
game. The most complicated moment in the process
of production is when the numbers come on the stones.
Karl's 21-tiling allows to play **Ewn without numbers**
on the stones:
When you role some number t, you have to move a stone
that is currently placed on a square of size t. When
you do not own such a stone you have to move the largest
possible smaller number or the smallest possible larger
number.

### The Rules for Two Players

Each player has six stones in the beginning, placed in his
home corner, on the little squares of size 1, 2, 3, 3, 4, 5.
The next diagram shows the starting position.
Black starts in the north-west corner, White starts in the
south-east corner. White is winner when one of his stones
reaches the square in the north-west corner of the board.
Analogously, Black is winner when one of his stones
reaches the square in the south-east corner of the board.

The players move in turn. White is to start, or the player
who lost the previous game. A move consists two parts:
rolling the 6-sided die, and moving an "admissible" stone.

When you role some number t, you have to move a stone
that is currently placed on a square of size t. When
you do not own such a stone you have to move the largest
possible number smaller than t or the smallest possible
number larger than t.
Example for the starting position:
of a single
forward step of an own stone. When there is some other stone
on the target square of the move this stone is taken off
the board. This happens also if this stone belongs to the
player himself.

Forward directions
for Black are to the East and to the South. Forward
directions for White are to the North and to the West. There
are not diagonal steps, due to the "special" structure of
the board.

### Karl's Race with Four Players

In case of four players two teams are formed. In this version each player has only four stones.
The team partners start in opposing corners. A team has
won when one player reaches the opposing corner with one
of his stones. In contrast to the classical "Ewn quattro"
a team has not lost when one member is reduced to zero
stones. Instead, this player simply passes when it is his
turn.
In honour of **Karl Scherer** I named this game
**Karl's Race**.

See also the board game
**Schneider von Gent**.

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