Vrijeme: 11:06

Četverodimenzionalna komba | 4D Combinatorics #4

Kao svoju posljednju četverodimenzionalnu konstrukciju, Karlo je ponovno počeo razmišljati o 10 \times 10 \times 10 \times 10 hiperkocki.

Karla sada konkretno zanima, koliko različitih hiper-pravokutnika (hiperkocaka koje nemaju nužno sve stranice jednakih duljina) se nalazi u hiperkocki koju promatra.

Note: hiper-četverokuti s, naprimijer, dimenzijama 1\times 2 \times 3 \times 4 i 2 \times 1 \times 4 \times 3 se uzimaju kao isti hiper-četverokut.

As his final four-dimensional construction, Karlo once again began thinking about a 10\times 10\times 10\times 10 hypercube.

Karlo is specifically interested in the following: how many distinct hyper-rectangles (hypercubes which do not necessarily have all edges of equal length) are contained within the hypercube he is observing?

Note. Hyper-rectangles with dimensions, for example, 1\times 2\times 3\times 4 and 2\times 1\times 4\times 3 are considered the same hyper-rectangle.