MathNet 2022-part-03 — 197 problems (EN–VI) Question 192

In a $3 \times 2$ rectangle, we put the numbers $1$ to $6$ in the squares in such a way that each number occurs exactly once. The *score* of such a distribution is determined as follows: for each two adjacent squares we compute the difference between their two numbers and we add up all these differences. In the example on the right, the differences are indicated in red. This distribution has score $17$.
What is the smallest possible score of such a distribution?