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Add down to One (Posted on 2003-05-21) Difficulty: 3 of 5
The numbers 0-9 are lined up in a row, like this:

0 1 2 3 4 5 6 7 8 9

You have to put in + and - signs in the blanks, so that in the end it will all equal 1.

Also, if possible, try to make expressions resulting in 0 and -1.

See The Solution Submitted by Jonathan Waltz    
Rating: 2.5000 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Solution | Comment 10 of 16 |
(In reply to re: Solution by Dave Neary)

Dave, I agree with you completely. All we have to do is to find subsets of (0,1,....,9) which add up to 22, and minus them.

It just so happens that there are 23 such subsets:

{6,7,9},{5,8,9},{4,5,6,7},{3,5,6,8},{3,4,7,8},{3,4,6,9},{2,5,7,8},{2,5,6,9},{2,4,7,9},{2,3,8,9},{2,3,4,6,7},{2,3,4,5,8},{1,6,7,8},{1,5,7,9},{1,4,8,9},{1,3,5,6,7},{1,3,4,6,8},{1,3,4,5,9},{1,2,5,6,8},{1,2,4,7,8},{1,2,4,6,9},{1,2,3,7,9},{1,2,3,4,5,7}

Reversing the signs in any solution for +1 gives us a solution for -1.

PS: Sorry to point it out Dave, but contrary to your suggestion {1,2,3,8,9} is not one such group. Obviously an oversight.
  Posted by Sanjay on 2003-05-22 05:29:24

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