Five numbers, two colors, and a single rule about sums. There seem to be many ways to distribute the colors, but every choice immediately constrains the next ones.
Five Numbers, Two Colors
Riddle statement
Color each of the numbers
\{1,2,3,4,5\}
red or blue.
A coloring is valid if there are no numbers \(x,y,z\) of the same color satisfying:
x+y=z.
The numbers \(x\) and \(y\) are allowed to be equal. For example, the relation
1+1=2
must also obey the rule.
Does a valid coloring exist?
Also determine whether \(5\) is the first impossible size: can \(\{1,2,3,4\}\) be colored validly?