## Happy New Year!

– 10*9*8+7+6-5+4*321 Happy New Year!
– It is a bit late for that!
– May be, but isn’t it beautiful?!
– That 10*9*8+7+6-5+4*321 = 2012?
– Yeah, I bet you it does not happen every year!
–  How long will it be until another year arrives that can be similarly expressed?
– You mean with interspersing +, -, *, /, or nothing between the numbers in order from 10 to 1?
– Yes.
– May be in one thousand years.
– That is a long time. Amazing!

Problem source: The Museum of Mathematics and the Wolfram Blog.

### 3 Responses to “Happy New Year!”

1. 2012 = [ (1+0+9)+(8+7)*(6+5)*4 ] * 3 + 2*1
2013 = [ (1+0+9)+(8+7)*(6+5)*4 ] * 3 + 2 + 1
2014 = {(1+0+9)*[(8+7+6)*5-4] – 3} *2*1
2015 = (1+0+9+8)*7*(6+5+4+3-2) – 1
2016 = (1+0+9+8)*7*(6+5+4+3-2)*1
2017 = (1+0+9+8)*7*(6+5+4+3-2) + 1

Found using a program I’d already written, to solve problems just like this one. The first operation it tries is addition, hence the preference for expressions that start with a chain of additions of single-digit numbers.

2. Using just 987654321:
2012 = 9*8*7*(6-5)*4 -3-2+1

Some delights for future years:
2013 = (65-4)*(32+1)
2015 = 8*(7+6+5)*(4+3)*2 – 1
2016 = (7+6-5)*4*3*21
2017 = 8*(7+6+5)*(4+3)*2 + 1

3. Jan Nordgreen says:

And one may use Mathematika:
http://blog.wolfram.com/2012/02/02/happy-109876-54321/