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 Forum index » Diversions » The Master Theorem
Thanksgiving riddle
Moderators: Cougar Draven
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die_kale
Greenhorn

Joined: 11 Nov 2011
Posts: 4
Location: Rotterdam

 		Thanksgiving riddle
So there is no new theorem at midnight tonight, just a riddle. I recon I bruteforced it using this formula in a spreadsheet:

Spoiler (Rollover to View):
=IF(TRUNC(COLUMN(A2)/ROW(A2))-COLUMN(A2)/ROW(A2)=0,A1*-1,A1)


So that gives me the requested value of bulb 64, and the number of lighted bulps...

ideas anyone?

PostPosted: Wed Nov 23, 2011 3:21 pm
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Rogi Ocnorb
I Have 100 Cats and Smell of Wee


Joined: 01 Sep 2005
Posts: 4244
Location: Where the cheese is free.

 		I get
Spoiler (Rollover to View):
10

Bulbs lit after 100 people

Specifically, bulb numbers:
Spoiler (Rollover to View):
That are perfect squares


And, bulb 64 is:
Spoiler (Rollover to View):
One of those


Edit:
How about some more stats?

Easier...
We know that bulb 1 spends the most time on (100%)
Which bulb spends the least time on and what percentage of time is it on?

Harder...
We know person 1 ends their turn with the most lights on (100).
Who ends their turn with the least lights turned-on and how many?
_________________
I'm telling you now, so you can't say, "Oh, I didn't know...Nobody told me!"


PostPosted: Wed Nov 23, 2011 4:09 pm
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mr. sunshine
Boot

Joined: 01 Jul 2011
Posts: 17
Rogi Ocnorb wrote:
I get
Spoiler (Rollover to View):
10

Bulbs lit after 100 people

Specifically, bulb numbers:
Spoiler (Rollover to View):
That are perfect squares


And, bulb 64 is:
Spoiler (Rollover to View):
One of those


Edit:
How about some more stats?

Easier...
We know that bulb 1 spends the most time on (100%)
Which bulb spends the least time on and what percentage of time is it on?

Harder...
We know person 1 ends their turn with the most lights on (100).
Who ends their turn with the least lights turned-on and how many?



My answer to your first:
Spoiler (Rollover to View):

The bulb that is on the lowest percentage of the time would be the second one. It is extinguished during the second person's walk and never illuminated again. Do we call that 1%, then?


And to your second:
Spoiler (Rollover to View):

The second to the last person ends their turn with the least lights on. Persons 82-99 are all turning lights off, while person 100 turns the last light on. The penultimate person leaves nine lights on.


PostPosted: Wed Nov 23, 2011 5:05 pm
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Rogi Ocnorb
I Have 100 Cats and Smell of Wee


Joined: 01 Sep 2005
Posts: 4244
Location: Where the cheese is free.

 		Give the man a see-gar!
_________________
I'm telling you now, so you can't say, "Oh, I didn't know...Nobody told me!"


PostPosted: Wed Nov 23, 2011 5:08 pm
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