+817 (1) Let $a_1,$ $a_2,$ $a_3$ be real numbers such that
\[|a_1 - a_2| + 2 |a_2 - a_3| + 3 |a_3 - a_1| = 1.\]
What is the largest possible value of $|a_1 - a_2|$?
(2) Let $a_1,$ $a_2,$ $a_3,$ $\dots,$ $a_{10}$ be real numbers such that
\[|a_1 - a_2| + 2 |a_2 - a_3| + 3 |a_3 - a_4| + 4 |a_4 - a_5| + \dots + 9 |a_9 - a_{10}| + 10 |a_{10} - a_1| = 1.\]
What is the largest possible value of $|a_1 - a_6|?$
