How Many Tribbles?

Assuming I haven’t made a mistake in time zone calculations, this post should go online exactly 50 years after the intrepid crew of USS Enterprise appeared on American screens for the first time. Since then, the adventures of Starfleet officers have been depicted in six TV series and 13 movies. Even though newer Treks are in many ways better, The Original Series will be forever beloved for its unique charm. Here is the opening of The Man Trap, the exact episode that aired 50 years ago:

Anyway, this is a math blog, so I should write about the math of Star Trek. This is a broad topic, and I decided to only discuss one scene, which involves tribbles. Tribbles are funny little creatures famous for being infallible Klingon detectors and notorious for reproducing way too fast. Soon after Deep Space Station K-7 was infiltrated with them, Kirk discovered a population living in a grain storage tank:

Spock estimated that the tank contained 1,771,561 tribbles under the assumptions that a single tribble had entered the tank three day before and had been producing a litter of 10 every 12 hours since then. Knowing Spock, it is hard to imagine him solving such a simple problem incorrectly, but let’s confirm his result anyway.

When a tribble produces a litter of 10, the number of tribbles multiplies by 11 (10 for offsprings + 1 for original tribble). They had just enough time for 6 reproduction cycles, so we would expect to have 116 tribbles, which is exactly the number that Spock arrived at. Great!

If you want to learn more about the math of Star Trek, I recommend an excellent video by James Grime:

If you want to solve a Star Trek-themed cipher, go check it out.

Finally, if you want to celebrate the anniversary of Star Trek in another brilliant way,

Engage!

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