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2012 Tricks

Discussion in 'Mathematics' started by DM, Jan 2, 2012.

  1. DM

    DM New commenter

    Just made it up for you.
    2012 is the product of a square number and a prime number.
    What was the last year that was a product of a square and a prime?
    When is the next year?
     
  2. DM

    DM New commenter

    My question is improved by excluding 1 x 2011 as a solution!
     
  3. Thanks for that!
     
  4. BillyBobJoe

    BillyBobJoe Established commenter

    How? Surely the product of 1 and 2011 is 2011?
     
  5. DM

    DM New commenter

    Just change the question slightly.
    2012 is the product of a prime and the square of a prime.
    When was the last time this happened?
    When is the next?
     
  6. DM

    DM New commenter

    And a contexualised version:
    Twin sisters Carly and Danielle were born on 1st January 2012. 2012 is the
    product of a prime number and the square of a prime number.

    Their twin
    brothers Alec and Ben were born on 1st January in the last year like
    this.

    What do you notice about the sum of the ages of all four children
    in the next year like this?

     
  7. lunarita

    lunarita Established commenter

    Ooh, thanks for this.
    I am in one of those moods where I am fretting about pointless things. This will prove a useful distraction this evening.
     
  8. dm - you are awesome!
     
  9. 007maths

    007maths New commenter

  10. ian60

    ian60 New commenter

    2012 looks like it could be a base 3 number.

    If it was, it would be equal to (2x27)+(0x9)+(1x3)+(2x1)=59 in base 10
    Which is prime.

    But 2012 'looks' even, and even numbers (other then 2) are not prime. What do even numbers look like in base 3.

    Maybe a bit convoluted and a too tenuous?
     
  11. In any odd base the digit sum of an odd number is odd. You can generalise this a bit too.
     

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