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(1) Let a1, a2, a3 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 a1, a2, a3, \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|?

 Apr 1, 2024
 #1
avatar+577 
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(1) The answer is 50.

 

(2) The answer is 20.

 Jun 27, 2024

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