Open Middle®
Directions: Using the digits 1 through 9 at most one time each, fill in the boxes to create a rectangular prism with a volume that is greater than 100 cubic units. What’s the least volume? What’s the greatest volume?
Hint
How might starting at the least (or greatest) dimension/factor help you think about this problem?
Answer
There are several possibilities.
• 4 x 6 x 8 = 192
• 3 x 8 x 9 = 216
• 6 x 8 x 9 = 432
• 4 x 6 x 8 = 192
• 3 x 8 x 9 = 216
• 6 x 8 x 9 = 432
Source: Kari Frazier
Greatest=504 units cubed
Least=120 units cubed
What factores did you use to get 120?
I thought it was tricky using the digits 1 through 9 at most one time each.
Those would only work if you could use the digit 0. I added that as an extension.
Greatest volume: 9 * 8 * 6 = 432
Least volume: 4 * 6 * 8 = 192
All possible solutions:
3 * 8 * 9 = 216
3 * 9 * 8 = 216
4 * 6 * 8 = 192
4 * 8 * 6 = 192
6 * 4 * 8 = 192
6 * 8 * 4 = 192
6 * 8 * 9 = 432
6 * 9 * 8 = 432
8 * 3 * 9 = 216
8 * 4 * 6 = 192
8 * 6 * 4 = 192
8 * 6 * 9 = 432
8 * 9 * 3 = 216
8 * 9 * 6 = 432
9 * 3 * 8 = 216
9 * 6 * 8 = 432
9 * 8 * 3 = 216
9 * 8 * 6 = 432
Why didn’t you use 9*8*7?? it would have given you 504 as the largest volume. and 9*6*2 would have given you a least volume of 108
You weren’t allowed to use 0 in your choices.
We got 3*5*7=105
9*8*7=504
What are your thoughts?
I had worked out this, and somehow I tried, it is probably wrong but my answer is 6 x 8 x 9 = 432 is the greatest, other is 4 x 6 x 8 = 192 which results in that being less than 432. Hope am right!