How can the digits 1 through 5 be arranged in the box to make the greast products?
The box is 2 row x 3 column. The first bottom column marked with "x".
To find the arrangement of the numbers 1 through 5 that would give the greatest product in the box with 2 rows and 3 columns, we need to consider two factors: the positioning of the digits and the order in which they are placed.
First, let's list all possible arrangements of the digits 1 through 5 in the box:
1 x x
2 3 4
1 x x
2 4 3
1 x x
3 2 4
1 x x
3 4 2
1 x x
4 2 3
1 x x
4 3 2
2 x x
1 3 4
2 x x
1 4 3
2 x x
3 1 4
2 x x
3 4 1
2 x x
4 1 3
2 x x
4 3 1
3 x x
1 2 4
3 x x
1 4 2
3 x x
2 1 4
3 x x
2 4 1
3 x x
4 1 2
3 x x
4 2 1
4 x x
1 2 3
4 x x
1 3 2
4 x x
2 1 3
4 x x
2 3 1
4 x x
3 1 2
4 x x
3 2 1
Looking at the arrangements, we can see that the "x" marked column can be filled with any of the remaining 3 digits (2, 3, or 4) since the aim is to maximize the product. However, to simplify the calculation, let's assume we place the largest remaining digit (4) in the "x" column.
Out of the 3 remaining digits (1, 2, and 3), we can place any of them in the top-left position (above the 4). Again, to maximize the product, let's place the largest remaining digit (3) in this position.
Now, to calculate the product for this arrangement:
3 x x
4 2 1
The product is: 3 * 4 * 2 * 1 = 24
Therefore, by arranging the digits 1 through 5 as shown above, we can achieve the greatest product of 24 in the given box.