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.