Problem #10
Two friends buy a open chain of beads (i.e. the chain is not a closed loop).
There are two colors of beads, black and white, and there are an even number
of each type. The friends would like to cut the chain so that each of them
gets an equal number of white beads and an equal number of black beads. What
is the smallest number of cuts that will guarantee this regardless of the
configuration of black and white beads in the chain? Please give some
indication as to why your answer is correct; don't just give a number.
What if there are more than two friends? (Again assuming that the number
of black beads and white beads allows them to be evenly distributed among
the friends.)
What if there are more than two colors of beads?
What if there are more than two friends and more than two colors?