Black Pearl
Posted in Pocet Knives on 04/11/2010 09:07 pm by Blade RunnerBlack Pearl
How to divide a black and white pearl necklace Puzzle!?!?
Find the solution for the following: Two robbers steal a valuable necklace of black and white pearls. There are even numbers of white and black pearls in the necklace. The pearls are evenly spaced, however, the colors are not necessarily alternating or even symmetric.
Provide a convincing argument that no matter what the necklace looks like, it is always possible to cut it into two pieces each having half the black and half the white pearls.
consider a vertical diametrical cut AB [imaginary]
from top to bottom in between beads
let us focus on one colour, say white pearls and on one half,
say clockwise between A & B [ THE half ]
suppose THE half contains less than half the white pearls
it is obvious that if the imaginary cut is rotated through 180°,
THE half will now contain more than half the white pearls
rotate the cut clockwise bead by bead [ a MOVE]
a MOVE may result in
(a) no change [ 0 decrease in deficit]
(b) an increase in deficit [ -1 decrease in deficit]
(c) a decrease in deficit [ 1 decrease in deficit]
one MOVE can reduce the deficit by a MAXIMUM of one,
so it follows that in moving from a deficit state to a surplus state,
there has to be a cut where there is neither deficit nor surplus
make the imaginary cut real at this point !
Scotty - The Black Pearl (Dave Darell Remix)
