Amida frameworks are compound ladders like the one shown in the
diagram with any number of uprights and any number of horizontal
rungs, no two rungs having a common endpoint. The winning position
is marked at the foot of one of the uprights. A path is marked
going downwards from the top of each upright. When coming to a rung
the path goes across and continues on down the adjacent upright. A
winning position is given at the foot of one of the uprights and in
the illustration player number 2 wins.
Draw your own frameworks and fill in the positions where the
players finish up at the bottom of the uprights. What do you
notice? Can you prove your observation?
Amida is used for drawing lots and it works equally well for any
number of players. The judge draws a framework on a piece of paper
with one upright for each player and marks 'winning positions' at
the foot of one or more of the uprights. The paper is rolled up
without giving the players time to study the diagram leaving the
tops of the uprights showing at the edge of the roll. Each player
chooses a different upright and writes his or her name on it. The
paper is then unrolled, the paths charted and the results declared.
Can you prove that no two paths ever end up at the foot of the same
Is it always possible for a player to win if he or she is
allowed to put in just one extra rung? If you think it is not
always possible draw your own framework to show this.