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.
March 7th, 2012 at 9:37 am
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.
March 7th, 2012 at 10:04 am
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
March 7th, 2012 at 10:43 pm
And one may use Mathematika:
http://blog.wolfram.com/2012/02/02/happy-109876-54321/