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Topic: 10x10 Vending Machine (Read 2435 times) |
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mattian
Senior Riddler
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10x10 Vending Machine
« on: Jul 12th, 2012, 12:47pm » |
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Suppose you have a vending machine containing a single product. The vending machine has 10 columns with 10 units in each column for a total of 100 units. The vending machine is full and you have sufficiently many coins to buy all the items in the machine. There is a fixed probability (p) that the vend will fail - this probability is per vend. If a vend fails, the remaining items in the selected column are blocked and the column becomes unusable. To vend an item you are free to select any column that isn't blocked or empty. Is there a particular strategy that can decrease the total loss (or blocked product) left in the machine? Or does it make no difference which column you choose? For instance - is there a benefit to always choosing the shortest column? Or the longest column?
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« Last Edit: Jul 12th, 2012, 12:50pm by mattian » |
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towr
wu::riddles Moderator Uberpuzzler
Some people are average, some are just mean.
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Re: 10x10 Vending Machine
« Reply #1 on: Jul 12th, 2012, 1:06pm » |
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It doesn't matter. Order of picking columns doesn't matter, because if each vend is independent, then each column is independent. So it doesn't matter whether you first empty one column and then another or switch back and fro. Also, welcome back; been a few years, hasn't it.
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« Last Edit: Jul 12th, 2012, 9:58pm by towr » |
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Grimbal
wu::riddles Moderator Uberpuzzler
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Re: 10x10 Vending Machine
« Reply #2 on: Jul 17th, 2012, 8:54am » |
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Yeah. It is like if you had 10 separate vending machines.
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