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.

0+1+2+3-4-5-6-7+8+9=1
0+12-3+4+5+6-7-8-9=0
0-1-2-3+4+5+6+7-8-9=-1
Obviously, if an expression can be made to equal a positive number, the same expression with all signs reversed will equal the negative of that number.

Carrying on:
0+12-3+4+5-6+7-8-9=2
0+1+2-3+4-5-6-7+8+9=3
0+12-3+4+5-6-7+8-9=4
0+1+2-3-4+5-6-7+8+9=5
0+12-3+4-5+6-7+8-9=6
0+1+2-3-4-5+6-7+8+9=7
0+12-3-4+5+6-7+8-9=8
0+1+2+3+4-5-6-7+8+9=9
0+12+3+4+5+6+7-8-9=10

I think a good question now would be: what is the first positive integer that cannot be achieved by adding + and - signs to the digits 0 through 9?

Posted by Bryan on 2003-05-21 04:57:12