(10) The minimum value of the function $y=|x-1|+|x-2|+\cdots+|x-10|$ is
(10) 25 Hint: We have
$$
|x-1|+|x-10| \geqslant|(x-1)-(x-10)|=9,
$$

and equality holds when $x \in[1,10]$. Similarly, $|x-2|+|x-9| \geqslant 7, \cdots$, $|x-5|+|x-6| \geqslant 1$, and equality holds respectively when $x \in[2,9], \cdots, x \in[5,6]$. Therefore,
$$
y \geqslant 9+7+\cdots+1=25,
$$

and equality holds when $x \in[5,6]$. Hence, the minimum value sought is 25.