Sum based on sub-sums

Question

Let's say, we have three numbers: $a, b, c$

but we know only their sums: $x = a + b, y = b + c.$

Is it possible to find sum $z = a + b + c$?

edit - $a, b, c$ are natural numbers

score 1 · Answer 1 · answered Jan 27 '16 at 15:35

1

No.

For example, take $x=y=0$.

Then, taking an arbitrary value of $a$, you can set $b=-a$, $c=a$ and you will have $x=y=0$ and $z=a$.

answered Jan 27 '16 at 15:35

5xum

123,496
6
128
204

thanks, you're right. But what if a, b, c are natural? – user251405 Jan 27 '16 at 15:37
@user251405 Still no. Except in some special cases, like $x=y=0$, where clearly $a=b=c=0$. – 5xum Jan 27 '16 at 15:46

score 1 · Accepted Answer · answered Jan 27 '16 at 16:01

1

Express a and c in term of b. (i) a=x-b (ii) c=-b+y. Substitute in z, z=(x-b)+b+(-b+y). The natural number b determine the solution triplet (a,b,c). How many solutions b can we have? Any natural number smaller than min(x,y) will do.

answered Jan 27 '16 at 16:01

user155673

338

Sum based on sub-sums

2 Answers2