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There is a math joke that floats around the internet every once in a while that goes something like . . . A mathematician and her infinitely many friends decide to stop by their favorite bar. The first mathematician orders 1 beer, the second orders 1/2 a beer, the third orders 1/4 a beer, the fourth orders 1/8 a beer, the fifth orders 1/16 a beer. . . it’s at this point the bartender, knowing a little math herself, interrupts and says "Fine, I’ll just pour you two beers.". How many beers should the bartender pour if the first mathematician orders 6 beers, the second orders 2 beer, the third orders 2/3 a beer, and so on?

User Jlos
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Answer:

  • Three beers.

Explanation:

The first mathematician orders 1 beer, the second orders 1/2 a beer, the third orders 1/4 a beer, the fourth orders 1/8 a beer, the fifth orders 1/16 a beer. . .

  • The Sequence is:
    1,(1)/(2), (1)/(4), (1)/(8), (1)/(16) \cdots
  • On observation, the next term is derived through the division of the previous term by 2.
  • 2 is the constant factor
  • Therefore, the bartender says 'Fine, I’ll just pour you two beers.'

Therefore, if the first mathematician orders 6 beers, the second orders 2 beer, the third orders 2/3 a beer, and so on

  • The sequence is
    6,2,(2)/(3), \cdots
  • On observation, the next term is derived through the division of the previous term by 3.
  • 3 is the constant factor
  • Therefore, the bartender should pour three beers.

User Sakhri Houssem
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