Cake number - Printable Version +- MKLab (https://mklab.gr) +-- Forum: [INDEX] (https://mklab.gr/forumdisplay.php?fid=1) +--- Forum: MATHEMATICS (https://mklab.gr/forumdisplay.php?fid=3) +---- Forum: ARTICLES (https://mklab.gr/forumdisplay.php?fid=13) +---- Thread: Cake number (/showthread.php?tid=671)

Cake number - mklabgr - 06-23-2026 Cake number Summary The cake number is a fascinating concept in combinatorics that describes the maximum number of pieces a three-dimensional cake (or cube) can be divided into using a given number of straight planar cuts. The idea is simple: each new cut should be placed so that it intersects all previous cuts in the most efficient way, creating as many new pieces as possible.  Starting with one whole cake, the sequence of maximum pieces grows as 1, 2, 4, 8, 15, 26, 42, and so on. For example, while three cuts can produce 8 pieces, a fourth cut cannot double that number to 16; the best possible result is 15 pieces. This problem is the three-dimensional counterpart of the famous “lazy caterer’s sequence,” which studies the maximum number of pieces a pizza can be cut into with straight cuts. ARTICLE