Dummy's Walkthrough of the Stacking Boxes Problem | WontonST

Dummy's Walkthrough of the Stacking Boxes Problem | WontonST

The stacking boxes problem is a problem that looks really complicated at a first glance but later turns out to be quite simple. You are given n boxes each of k dimensions to figure out the maximum number of box-in-box chains (called nested boxes) you can form.

Understanding k-Dimensions

If I said "visualize a 8 dimensional box" you would be stumped. Let's not even try to go there. Let's start with a 3-D cube. If the dimensions are (4,2,1) we realize that if we rotate it we can get any permutation of the three numbers (1,4,2), (2,1,4), (2,4,1), (1,2,4), (4,1,2). This is good news because now we don't care how many dimensions the box because no matter what dimension, we can always move the numbers around.

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