stumbled upon the following problem:
a circular disk is cut into n distinct sectors each shaped like a piece of pie and all meeting at the center point of the disk.Each sector is to be painted red,green,yellow,or blue in such a way that no two adjacent sectors are painted the same color. Let Sn be the number of ways to paint the disk. Find a recurrence relation for Sk in terms of Sk-1 and Sk-2 for each integer k>=4.
Anybody can explain step by step how to solve this? any help appreciated stumbled upon the following problem:
a circular disk is cut into n distinct sectors each shaped like a pie
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maybe a tree or graph problem - they lend them selves well to recursive solutions. each section has two neighbors. pick one section to be the root then its neighbors are the next 'level' then each neighbor has two neighbors ..... if you draw the diagrams, it might help to puzzle out the recurrence relationship.
graph i think rather than a tree
Also sounds a lot like CSP (Constraint Satisfaction Problem), one common example is the "map coloring problem" which is also associated with the "four color theorem".
Here are a few links on this that you may or may not be interested in.
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solving the problem computationally seems to be well documented with plenty of possible algorithms / models to start off with.
but actually writing the recurrence relation as specified in the OP? was there more information? seems like the question is not asking for a recurrence relation for solving the problem but for defining different possible solutions - that almost sounds like the same thing but ..... if you can write the recurrence relation for all possible solutions then would you be able to use it to code a single solution?