Dr. Troy
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« Reply #2 on: October 06, 2010, 01:59:21 PM » |
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Hey Bama - tricky game here, as the initial distribution possibilities seem to allow for a lot of movement, but I think you'll find that as we begin to consider the rules those distributions get much more limited. Here's what we know:
We have 9 variables (three each of O, P, S) to distribute to the Mon-Fri base. This sounds like a 9 --> 5 distribution, but we don't necessarily have to have a batch on each day, so it's a bit less defined here. That is, with the rule about no cookie is made twice on the same day (rule 1), we need to have at least three days to distribute all of the cookies: 3-3-3 (all three types together on three of the five days), but we don't know that we'll need to have a batch on every single day.
And when you consider the third rule that the 2nd O batch is on the day of the 1st P batch, that spreads the batches into at least four days, since it means the three sets of three can't overlap perfectly. It also means that the "at least one batch on Monday" (rule 2) must be O or S.
The final rule about the 2nd S on Thursday means that the 3rd S must be Friday, and things become even more limited.
Now consider: you have that block with O2 and P1, and it must be either Tuesday (forcing O1 Monday), or Wednesday (forcing P2 and P3 Thursday and Friday). That's pretty restricted, as well.
So using your days as your base, you can have that O/S option Monday, S on Thurs and Fri, and you know that the O2/P1 block is either Tuesday or Wednesday, which then controls other variables as well. Beyond that there's still a fair amount of movement possible concerning the number of batches each day (only Monday is limited to 2, which answers 14), so pay attention to the movement of that block and how it controls the placement of other batches.
Good luck!
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