# 2012 Tricks

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

1. ### DMNew 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. ### DMNew commenter

My question is improved by excluding 1 x 2011 as a solution!

3. ### mathmo2000

Thanks for that!

4. ### BillyBobJoeEstablished commenter

How? Surely the product of 1 and 2011 is 2011?

5. ### DMNew 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. ### DMNew 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. ### lunaritaEstablished 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. ### florapost

dm - you are awesome!

10. ### ian60New 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. ### Null

In any odd base the digit sum of an odd number is odd. You can generalise this a bit too.