A String Of Sweets
A possible configuration (left) and a possible division scheme (right)
Alice and George have bought a long strip of candies, with three different flavors (orange, strawberry, blueberry) of candies stringed together in a random order on a piece of thread. The two would like to split up the candies by cutting the string into portions and sharing the portions between themselves. Furthermore, each must receive an equal number of each flavor of candy.
What is the minimal number of cuts that Alice and George would need for any such thread?
Assume that there is an even number of each candy flavor.
The answer is 3.
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1 solution
The problem is incredibly well explained and generalized in the following video:
Who (else) cares about algebraic topology? Stolen Necklaces and Borsuk-Ulam