To find the maximum difference possible by placing the digits 1, 3, 5, 7, and 9 in the boxes, you can follow these steps:
1. Place the largest digit, 9, in the leftmost box. This maximizes the difference because a higher number at the start contributes more to the overall value.
2. Place the next largest digit, 7, in the second box from the left. This further increases the difference.
3. Place the next largest digit, 5, in the middle box. This helps maintain the gap between the numbers on both sides.
4. Place the next largest digit, 3, in the second box from the right.
5. Place the smallest digit, 1, in the rightmost box.
By following this arrangement, with 9 in the leftmost box and 1 in the rightmost box, you create the largest possible difference. The difference between the number formed by the leftmost boxes (975) and the number formed by the rightmost boxes (31) is 944.
Therefore, the maximum difference achievable by arranging the digits in this way is 944.
