How to approach this problem: "You run a boarding house with 90 rooms..."

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jgraham1997

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You run a boarding house with 90 rooms. You have 100 regular guests. On anygiven night a random selection of exactly 90 of your regular guests will show up, each needing a single room.You want to distribute a set of keys to the guests permanently in such a way that no matter which 90 guestsshow up on a given night each one will be guaranteed access to a room. (One way to do this would be togive each of the 100 guests a key to each of the 90 rooms, but that would require you to distribute 9000keys.) What is the minimum number of keys you must distribute?
 
jgraham1997 said:
You run a boarding house with 90 rooms. You have 100 regular guests. On anygiven night a random selection of exactly 90 of your regular guests will show up, each needing a single room.You want to distribute a set of keys to the guests permanently in such a way that no matter which 90 guestsshow up on a given night each one will be guaranteed access to a room. (One way to do this would be togive each of the 100 guests a key to each of the 90 rooms, but that would require you to distribute 9000keys.) What is the minimum number of keys you must distribute?
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What are your thoughts?

Please share your work with us ...even if you know it is wrong.

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I unsure of where to begin to tackle the problem so have not got any work to post

I have considered some systematic distribution of the keys, but am unsure on how I am supposed to arrive at a value for the minimum numbers of keys to ensure every person has a room.
 
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jgraham1997 said:
I unsure of where to begin to tackle the problem so have not got any work to post

I have considered some systematic distribution of the keys, but am unsure on how I am supposed to arrive at a value for the minimum numbers of keys to ensure every person has a room.
Click to expand...
Maybe start from the number of keys you'll need on any given night.... (explained here) ;)
 
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