Final Answer:
The numbers 1, 7, 8, 9, and 10 can be placed in the boxes to achieve a total of 810.
Step-by-step explanation:
To solve the problem, we need to assign each number from 1 through 9 to the given boxes in a way that their sum is equal to 810. Starting with the given sequence 0, 4, 7, 9, 10, we can observe that 0 + 4 + 7 + 9 + 10 = 30. To reach 810, we need to add 780 more.
The numbers 1, 7, 8, 9, and 10 provide the required sum: 1 + 7 + 8 + 9 + 10 = 35. Multiplying this sum by 22 (the number of times the sequence 0, 4, 7, 9, 10 appears) gives us 770. Adding the remaining 10 (810 - 770) to the last number, 10, completes the sequence and results in a total of 810.
In mathematical terms, this can be expressed as:
\[ (0 + 4 + 7 + 9 + 10) \times 22 + 10 = 810. \]
Therefore, the solution is valid, and the numbers 1, 7, 8, 9, and 10 can be placed in the respective boxes to achieve the desired total of 810.