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 Tribbles in the hold
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Daddio
Male Advanced Member
775 Posts
[Mentor]


Calera, AL
USA

Suzuki

Bandit 1250

Posted - 10/03/2012 :  7:57 PM                       Like
Fun brain teaser -

I am a fan of the classic TV series Star Trek. From the episode "The Trouble with Tribbles" the crew encounters these cute little furball creatures called Tribbles. Given in the show, tribbles, when well fed produce a litter of ten new tribbles every 12 hours. They are hermaphrodites, each creature is able to reproduce on its own. One tribble was placed in a cargo hold full of grain and three days has elapsed. Spock says, "There are now 1,771,561 tribbles in the hold."

Is Spock correct? - Defend your answer.

twc
Male Advanced Member
836 Posts
[Mentor]


Fort Collins, CO
USA

Harley-Davidson

Electra Glide Ultra

Posted - 10/03/2012 :  11:02 PM
quote:
Originally posted by Daddio

Is Spock correct? - Defend your answer.
Of course he's correct! What kind of a question is that???

We are told that at period t0 we have one tribble in the hold.

Each tribble produces a litter of ten tribbles during each 12-hour period, plus the parent tribbles remain. Thus, the number of tribbles in the hold at period I is given by tI = 10 * tI-1 + tI-1 = 11 * tI-1

There are six twelve-hour periods in three days, so the number of tribbles will be:

Period 0 = 1 (start)
Period 1 = 11
Period 2 = 121 (one day)
Period 3 = 1331
Period 4 = 14,641 (two days)
Period 5 = 161,051
Period 6 = 1,771,561 (three days)

Editorial comment: In mathematical formulas, it should not be necessary to capitalize the letter "I".
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Daddio
Male Advanced Member
775 Posts
[Mentor]


Calera, AL
USA

Suzuki

Bandit 1250

Posted - 10/04/2012 :  6:10 AM
Nice logic, neatly presented.

A+ to twc

Math can be fun.
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kacinpa
Male Advanced Member
802 Posts
[Mentor]


Lansdale, PA
USA

Triumph

Sprint GT

Posted - 10/04/2012 :  9:20 AM
Star Trek + Math = Maximum Awesomeness!

Do you suppose they would reproduce at a different rate if the grain were other than Quadrotriticale?
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Daddio
Male Advanced Member
775 Posts
[Mentor]


Calera, AL
USA

Suzuki

Bandit 1250

Posted - 10/04/2012 :  8:34 PM
quote:
from kacinpa:
Do you suppose they would reproduce at a different rate if the grain were other than Quadrotriticale?


I would speculate that so long as they are well fed, the rate would remain the same regardless. I am not sure if they would like to be in a cooler of whatever worms Klingons consider good food, but I once again speculate an ample supply of edible grains would satisfy them regardless of type.
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