Question

Consider the set S={w,x,y,z}. If the set of all possible sums of any three different elements from S is {-1,3,5,8}, then what is the set S?

Answer 1

start adding 3 until you get 4

-1+3+5 = 7
-1+3+8= 10
5+3+8=16
8+5-1=12

Answer 2

w+x+y,
w+x+z,
w+y+z
x+y+z
-> 3w + 3x+3y+3z=15
-> w+x+y+z=5