Connecting computers and printers (combinatorics)

[Michal]

There are 15 computers and 10 printers in the computer room. Ten computers need a printer every 5 minutes, and only one computer can use the printer at a time. Make sure that at least 6 computers must be connected to each printer. Therefore, the minimum number of links required for each computer to have the printer available whenever it needs it is 60. Design a scheme with 60 links that suits your task.

 

[Deleted member 4993]

There are 15 computers and 10 printers in the computer room. Ten computers need a printer every 5 minutes, and only one computer can use the printer at a time. Make sure that at least 6 computers must be connected to each printer. Therefore, the minimum number of links required for each computer to have the printer available whenever it needs it is 60. Design a scheme with 60 links that suits your task.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

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Please share your work/thoughts about this problem.

 

[Michal]

I have tried to solve this task, but I got stuck at proving that at least 6 computers must be connected to each printer. I can design a scheme with 60 links that suits the task, but I do not understand why there must be at least 6 links.

 

[Steven G]

Please show us your work so we can give you hints on how to continue. If you followed the posting guidelines by posting your work you would have received help by now.

 

[Romsek]

The problem seems a bit underspecified. For example we aren't given any description of the length of each printing task.
We're told the computers need a printer every 5 minutes. Is this fixed in stone or is it the mean of a Poisson distributed rv describing
how often print events occurs?

Are you sure that the 6 connections per printer was actually derived somehow and not just specified?

 

[Michal]

Please show us your work so we can give you hints on how to continue. If you followed the posting guidelines by posting your work you would have received help by now.

But I have basically nothing done, that's why I didn't show you my work. I have only tried writing down 15 computers in one row and 10 printers in another row and tried to do some connections, but that's basically all have done so far. That's why I need help, because I'm stuck right at the beginning...

 

[Michal]

The problem seems a bit underspecified. For example we aren't given any description of the length of each printing task.

This is the task I was given, there were no more details about it. But I suppose the length of each printing task is supposed to be very short, maybe like printing one page each time.

We're told the computers need a printer every 5 minutes. Is this fixed in stone or is it the mean of a Poisson distributed rv describing
how often print events occurs?

This was a task for freshmen at the university and we haven't studied Poisson distribution yet, so I don't think that would be the case. I think it was meant, that every 5 minutes 10 random computers need a printer (for a very short time but all 10 at the same time).

Are you sure that the 6 connections per printer was actually derived somehow and not just specified?

Yes, by this I'm sure that it was derived, because the teacher told me that the 6 connections were her own calculations.

 

[Romsek]

Well... if all 15 computers have a print job at the same time, and there is no queueing of print jobs going on then this scheme won't work.
15 computers are going to demand immediate access to 10 printers and it will be Black Friday at Walmart.

It doesn't matter how many different computers are attached to to each printer.

There's just got to be more to all of this.