Question 167
Ayman writes down the numbers $1$ through $10$ in a sequence in some order, writes down the nine (positive) differences between adjacent numbers and computes the sum of these differences. The result is called the *dynamic* of the sequence. For example, the dynamic of the sequence $1, 2, 3, 4, 5, 6, 7, 8, 9, 10$ is $9$, and the dynamic of $2, 1, 3, 10, 4, 5, 9, 6, 8, 7$ is $1 + 2 + 7 + 6 + 1 + 4 + 3 + 2 + 1 = 27$.
What is the greatest dynamic that such a sequence with the numbers $1$ through $10$ can have?
A) $41$ B) $43$ C) $45$ D) $47$ E) $49$
What is the greatest dynamic that such a sequence with the numbers $1$ through $10$ can have?
A) $41$ B) $43$ C) $45$ D) $47$ E) $49$