Place the digits 1, 2, 3, 7, and 8 in the following boxes so that the greatest product is obtained

- - - X - -

The hundreds spot should have the largest digit and the tens spot in the the two digit number should have the second largest. Follow a similar principle for the remaining digits.

I hope this helps. Thanks for asking.

To find the greatest product using the digits 1, 2, 3, 7, and 8, we need to place the digits in such a way that the larger digits are multiplied together. Let's go step-by-step:

Step 1: Identify the two largest digits.

Based on the given digits, the two largest digits are 7 and 8.

Step 2: Place the largest digit in the leftmost box.

To obtain the greatest product, we want to maximize the value of the leftmost digit. So, we should place the digit 8 in the leftmost box.

8 - - X - -

Step 3: Place the second-largest digit in the second box.

To maximize the product, we want the second-largest digit to be multiplied with 8. Therefore, we should place the digit 7 in the second box.

8 7 - X - -

Step 4: Place the remaining digits in the remaining boxes.

To maximize the product further, we want to multiply the remaining digits in descending order. So, we should place the remaining digits (3, 2, 1) in the remaining boxes from left to right.

8 7 3 X 2 1

Step 5: Calculate the product.

Finally, calculate the product:

8 × 7 × 3 × 2 × 1 = 336

Therefore, by placing the digits 1, 2, 3, 7, and 8 in the given boxes, the greatest product obtained is 336.

To find the arrangement of the digits that gives the greatest product, we need to consider the values that will be multiplied with "X" in order to maximize the product.

Let's analyze the factors involved. We can see that "X" will be multiplied by two other digits. In order to obtain the greatest possible product, we want "X" to be multiplied by the largest digits available, which would be 7 and 8 in this case.

Therefore, to obtain the greatest product, we can place 7 and 8 in the remaining empty boxes. The arrangement would be:

- 7 8 X 1 2 3

Now, when we multiply "X" by 7 and 8 respectively, we will get the greatest product possible with the given digits.