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Hypercake NumberHypercake Number
Cake number, as defined in mathematics is the number of maximum pieces a cake can be cut into with a given number of cuts. In this post, we will try to do the same with a cake (a Hypercake if you may) in higher dimensions.

The Knife's Dimension

Before we move on to cutting cakes, let's ponder upon the dimension of the knife. What should be the dimension of the knife when cutting a multidimensional cake?

For a regular cake ($3$D), we use a regular knife (a $2$D plane).
For a cutting pa...