Let $x_1,x_2,\dots ,x_{50}$ be $50$ integers such that the sum of any $6$ of them is 24, then:

Question

Let $x_1,x_2,\dots,x_{50}$ be $50$ integers such that the sum of any $6$ of them is $24$, then which option is true

I am totally clueless how to proceed :(

Help appreciated :)

$x_1+x_2+x_3+x_4+x_5+x_6=x_1+x_2+x_3+x_4+x_5+x_7\implies x_6=x_7$. Can you take it from there? — lulu, Mar 29 '16 at 15:16
This question would make more sense if it asked for consecutive $6$ of them — Asinomás, Mar 29 '16 at 15:23
As another way to see it, the sum of the six greatest elements is the same as the sum of the six smallest, which gives the result. — Captain Lama, Mar 29 '16 at 15:23

score 4 · Accepted Answer · answered Mar 29 '16 at 15:18

4

The key part is that the sum of $\textbf{any}$ $6$ of the numbers must be $24$. Therefore, $$x_1=x_2=\dots=x_{50}=4$$

answered Mar 29 '16 at 15:18

J. Bush

1 Answers1