Let \(a_1,a_2,\) and \(a_3\) be real numbers such that \(|a_1 - a_2| + |a_2 - a_3| + |a_3 - a_4| + |a_4 - a_5| + \dots + |a_9 - a_{10}| + |a_{10} - a_1| = 500.\) What is the largest possible value of \(|a_1 - a_6|?\)
The largest possible value of |a_1 - a_6| is 100.
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