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Guest Message by DevFuse

# Unlocking doors

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Posted 07 February 2014 - 08:34 PM

You were recently hired to be the head of maintenance in a mathematics building.  The building has 61 doors but 60 our locked.  In your office you have ten keys.  Each key unlocks at least 1 door and no two keys unlock the same amount of doors nor the same door.  There are ten rooms on a floor, with your office being in the basement (for technically an eleventh floor).

1. Develop an optimal strategy that will quickly tell you how many doors each key unlocks.

2. Develop an optimal strategy that will quickly tell you which door each key unlocks (if different from #1).

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### #2 superprismatic

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Posted 07 February 2014 - 10:57 PM

I have 2 questions:

1.  Are we to find keys to open all 61 doors?  A door need not be locked for us to test a key to it.  Or are we

to find keys for only the 60 locked doors?

2.  If the basement is technically the eleventh floor, then there must be 10 floors above it with 10 rooms per floor.

That's a total of 100 rooms plus the office in the basement.  Is this correct?  If so, shouldn't each above-ground

floor have 6 rooms?  Otherwise, there would have to be 40 rooms without doors.

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### #3 TimeSpaceLightForce

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Posted 08 February 2014 - 12:19 AM

Spoiler for maintainance

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Posted 08 February 2014 - 05:06 AM

I have 2 questions:

1.  Are we to find keys to open all 61 doors?  A door need not be locked for us to test a key to it.  Or are we

to find keys for only the 60 locked doors?

2.  If the basement is technically the eleventh floor, then there must be 10 floors above it with 10 rooms per floor.

That's a total of 100 rooms plus the office in the basement.  Is this correct?  If so, shouldn't each above-ground

floor have 6 rooms?  Otherwise, there would have to be 40 rooms without doors.

Alas, the basics i miss.  yes. there are 6 rooms on a floor with the exception of the basement where there is only 1.  And yes, you need to find a key for the basement as well.

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### #5 bonanova

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Posted 08 February 2014 - 02:22 PM

What is the relation of the ten floors to optimality?

Is optimal fewest operations or shortest time?

Does it take time to travel between floors?

Are there n elevators ?

Are you initially inside your basement office?

If so can you open its door without first identifying its key and using it to get out?

Spoiler for since

This is a nice puzzle.

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Vidi vici veni.

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Posted 08 February 2014 - 03:29 PM

What is the relation of the ten floors to optimality?

Is optimal fewest operations or shortest time?

Does it take time to travel between floors?

Are there n elevators ?

Are you initially inside your basement office?

If so can you open its door without first identifying its key and using it to get out?

Spoiler for since

This is a nice puzzle.

What is the relation of the ten floors to optimality?

Is optimal fewest operations or shortest time?

optimal in the sense that i want to go to the fewest floors and fewest doors and testing the fewest keys possible.

Does it take time to travel between floors?

Are there n elevators   ?

travel time is not a consideration, we could use the exercise

Are you initially inside your basement office?

If so can you open its door without first identifying its key and using it to get out?

you start out in the basement which is unlocked.  but you do need to know what unlocks this door.

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### #7 phil1882

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Posted 08 February 2014 - 08:24 PM

Spoiler for aproaching a solution?

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### #8 bonanova

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Posted 09 February 2014 - 10:48 AM

optimal in the sense that i want to go to the fewest floors and fewest doors and testing the fewest keys possible.

So optimal means minimize the sum: floors+doors+ keys.

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Vidi vici veni.

### #9 TimeSpaceLightForce

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Posted 09 February 2014 - 02:53 PM

Spoiler for straight forward

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### #10 TimeSpaceLightForce

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Posted 09 February 2014 - 05:09 PM

Spoiler for more key sets

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