6.3. Can the numbers $1,2, \cdots, 10$ be written in a row in some order so that the sum of every three consecutive numbers is not greater than 15? Explain your reasoning.
6.3. Cannot.

The sum of all 10 numbers is 55. If the sum of any 3 consecutive numbers is not greater than 15, then the sum of the first 9 numbers is not greater than 45, so the 10th number is not less than 10, and thus, it must be 10. Similarly, the sum of the last 9 numbers is not greater than 45, so the 1st number is not less than 10, and therefore, it must also be 10. This is impossible.