White Necklace
White Necklace
How to divide Puzzle pearl necklace black and white?!?
Find a solution as follows: Two burglars steal precious necklace of black pearls and white. There's even a number of white and black pearls in the necklace. Pearls are evenly spaced, however, the colors are not always alternately or even symmetrical. Provides a convincing argument that no matter what looks like a necklace, it is always possible to cut into two parts each having a half black and half white pearl.
consider the straight vertical cut AB [fantasy] from top to bottom between the beads let us focus on one color, say white pearl and on one half, say in the direction clockwise between A & B [Half THE] half THE contain less than half white pearl it is clear that if the cut imaginary rotated through 180 °, half THE will now contain more than half of white pearls rotate clockwise cut beads by [MOVE a] MOVE can produce (a) no change [0 deficit reduction] (B) an increase in the deficit [-1 deficit reduction] (c) deficit reduction [1 decline in the deficit] one can reduce deficits by MOVE MAXIMUM of one, so it follows that in moving from state surplus to deficit countries, there should be a piece in which there is no deficit or surplus that makes the imaginary real cut at the moment!
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