by **GeradHum** » Wed Sep 20, 2023 2:41 pm

The formula you're using to calculate how many cubes can fit in a box is based on the ratio of areas, but it doesn't take into account the dimensions of the box and the cubes in a way that ensures they can be physically arranged inside the box. To accurately calculate how many cubes can fit inside a box, you need to consider both the area and the dimensions of the box and the cubes.

Here's a more accurate approach to calculate the maximum number of cubes that can fit inside a box:

Calculate the area of the box (BoxArea) by multiplying its width (bw) and height (bh).

Calculate the area of a single cube (CubeArea) by multiplying its width (cw) and height (ch).

Divide the BoxArea by the CubeArea to find the maximum number of cubes that can fit in the box.

However, to ensure that you're not overestimating the number of cubes that can fit, you also need to consider how the cubes are oriented within the box. For example, if the cubes are taller (height greater than width) and the box is wider (width greater than height), the cubes may not fit horizontally. Therefore, you should consider both the horizontal and vertical orientations of the cubes within the box.

Here's a modified formula that takes both dimensions and areas into account:

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MaxCubes = min(floor(bw / cw) * floor(bh / ch), floor(bw / ch) * floor(bh / cw))

This formula calculates the maximum number of cubes that can fit by considering both horizontal and vertical orientations and choosing the smaller of the two possibilities.

For example:

If the box is 2x2 and the cubes are 1x1, you would get MaxCubes = min(2 * 2, 2 * 2) = 4, which is correct.

If the box is 2x6 and the cubes are 4x4, you would get MaxCubes = min(0, 0) = 0, indicating that no cubes can fit in this configuration.

This formula should give you a more accurate result for calculating how many cubes can fit inside a box considering their dimensions and orientations.