File APIs for Java Developers
Manipulate DOC, XLS, PPT, PDF and many others from your application.
The moose likes Programming Diversions and the fly likes 1-1+1-1.. Big Moose Saloon
  Search | Java FAQ | Recent Topics | Flagged Topics | Hot Topics | Zero Replies
Register / Login

Win a copy of REST with Spring (video course) this week in the Spring forum!
JavaRanch » Java Forums » Other » Programming Diversions
Bookmark "1-1+1-1.." Watch "1-1+1-1.." New topic


Arjun Shastry
Ranch Hand

Joined: Mar 13, 2003
Posts: 1893
Each of a1,a2,a3..aN are either 1 or -1.
The expression S = a1*a2*a3*a4+a2*a3*a4*a5+....+aN*a1*a2*a3 = 0
(* means multiplication and a1*a2 means value of a1 multiplied by value of a2)
Prove that 4 divides N.
I have taken this from Problem Solving Strategies

Arjun Shastry
Ranch Hand

Joined: Mar 13, 2003
Posts: 1893
If sign of every a(i) is changed,nothing changes .If sign of two a(i)s are same and other two are of different,nothing changes.If sign of one or three a(i) are different then S changes by +-4.If all four a(i) are of same sign,then S changes by +-8.That means S is changing by +-4 or +-8.
S=0mod(4).But S = n hence 4 divides n.
I agree. Here's the link:
subject: 1-1+1-1..
It's not a secret anymore!