Question

There is an ample supply of identical blocks (as shown). Each block is constructed from four 1 × 1 × 1 unit-cubes glued whole-face to whole-face. What is the greatest number of such blocks that can be packed into a box that is 6 units tall, 7 units wide, and 8 units deep without exceeding the height of the box?

Answer 1

72

Step-by-step explanation:

The answer is 72 because my teacher gave it to me. I promise i'm legit, and I won't lie. This is the real answer, and if you choose 336, you're probably getting it wrong. That's from Math Olympiad.

Answer 2

The greatest number of identical blocks that can be packed into the given box without exceeding its height is 84.

Step-by-step explanation:

To determine the greatest number of identical blocks that can be packed into a box without exceeding the height of the box, we need to find the volume of both the block and the box.

Each block is constructed from four 1x1x1 unit cubes, so its volume is 4 cubic units.

The volume of the box is 6 units tall, 7 units wide, and 8 units deep, so its volume is 6x7x8 = 336 cubic units.

To find the greatest number of blocks that can fit in the box, we divide the volume of the box by the volume of one block: 336/4 = 84.

Therefore, the greatest number of blocks that can be packed into the box without exceeding the height is 84.