Question 16
There are $2n$ cards. On each card some real number $x$, $1 \leqslant x \leqslant 2$, is written (there can be different numbers on different cards). Prove that the cards can be divided into two heaps with sums $s_1$ and $s_2$ so that
$$
\frac{n}{n+1} \leqslant \frac{s_1}{s_2} \leqslant 1.
$$
$$
\frac{n}{n+1} \leqslant \frac{s_1}{s_2} \leqslant 1.
$$