You may also like  problem icon  Links and Knots   problem icon
The interval 0 - 1 is marked into halves, quarters, eighths ...
etc. Vertical lines are drawn at these points, heights depending
on positions. What happens as this process goes on indefinitely?
problem icon  Voting Paradox   Binary Sequences   Bill from
Reading School sent in this solution and other good solutions
came in from Jax from Pate's School and Curt from Reigate
College.  This problem can easily be solved through use of Georg
Cantor's method for proving that the set of irrational numbers
is uncountable. Suppose we tabulate the results of the coin-
flipping so that one set of infinite tosses is one row. We might
have something like this:  1) 0 1 0 1 1 1 0 0 0 0 1... 2) 10 0 1
1 0 1 0 1 0 1... 3) 1 1 1 0 0 1 0 1 0 0 0... and so on down and
across the infinite list.  Now, we take a diagonal line,
starting from the top left and going right and down. The first
three digits in this sequence would be 0 0 1. Suppose that this
diagonal line giv