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.
(In reply to
Solution by Sanjay)
The solution is easier than that.
0+1+...+9 = 45. We want to add +s and -s to make 1. Grouping all the +ed numbers and the -ed numbers together, we get
(a1+b1+c1+...) - (a2+b2+...) = 1
and
a1+b1+c1+...+a2+b2+... = 45.
The obvious solution to this is 23 - 22 = 1, 23 + 22 = 45 And in fact this is the only solution.
So to solve the problem we just need to take any subset of (0,1,...,9) which adds up to 22, minus them, and we're done.
One such group is 1,2,3,4,5,7 Another is 1,2,3,8,9, and so on.
Cheers,
Dave.
re: Solution
