What formula is used?

[Vanyel]

What formula is used by Spock and Dax top come up with the number of tribbles in The Trouble with Tribbles and Trials and Tribble-ations?

1,771,561 That's starting with one tribble with an average litter of ten every twelve hours over three days.

Just wanting to know.

 

[Sector 7]

You just quoted the formula.

 

[Vanyel]

You just quoted the formula.

That's how the formula works. But what is the actual formula used. I know X=1,771,561, but what is the actual mathematical formula? I was never good at word problems, so please, how do you get "X"?

 

[Biggshow]

Of course, it's just a joke line because the actual formula would be x=1+10 to the sixth power (there are 6 twelve-hour periods in 3 days), or 1,000,001. Maybe Spock and Dax had additional information that would have complicated the issue for the listener.

If the average litter was 11, that would give you a final total of 1,770,352 which is much closer to the final number quoted.

The real world explanation is that it's just a funny number.

 

[T'Girl]

start with ... one tribble (mother zero) with a litter of ten (or eleven) every twelve hours, you get:
00 hour ..... 1 / 1
12 hours .... 11 / 12
24 hours .... 110 / 132
36 hours .... 1,100 / 1,452
48 hours .... 11,000 / 15,972
60 hours .... 110,000 / 175,692
72 hours .... 1,100,000 / 1,932,612

however, Spock said: "And allowing for the amount of grain consumed and the volume of the storage compartment."

 

[Vanyel]

OK I found the formula:

x=11^(n/12) where n=total number of hours
x=11^(72/12)
x=11^6
x=1,771,561

The number does assume that every tribble had a litter of 10, no more, no less.

Link. Look under the topic "Production"

 

[Biggshow]

start with ... one tribble (mother zero) with a litter of ten (or eleven) every twelve hours, you get:
00 hour ..... 1 / 1
12 hours .... 11 / 12
24 hours .... 110 / 132
36 hours .... 1,100 / 1,452
48 hours .... 11,000 / 15,972
60 hours .... 110,000 / 175,692
72 hours .... 1,100,000 / 1,932,612

however, Spock said: "And allowing for the amount of grain consumed and the volume of the storage compartment."

Forgot about the mother.

 

[Rush Limborg]

OK I found the formula:

x=11^(n/12) where n=total number of hours
x=11^(72/12)
x=11^6
x=1,771,561

The number does assume that every tribble had a litter of 10, no more, no less.

Link. Look under the topic "Production"

Brilliant!

I knew it was 11^6, but...that was it.