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arXiv · 2511.15864

Cutting a Pancake with an Exotic Knife

David O. H. Cutler·Jonas Karlsson·Neil J. A. Sloane
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Abstract

In the first chapter of their classic book "Concrete Mathematics", Graham, Knuth, and Patashnik consider the maximum number of pieces that can be obtained from a pancake by making n cuts with a knife blade that is straight, or bent into a V, or bent twice into a Z. We extend their work by considering knives, or "cookie-cutters", of even more exotic shapes, including a k-armed V, a chain of k connected line segments, long-legged versions of the letters A, E, H, L, M, T, W, or X, a convex polygon, a circle, a phi, a figure 8, a pentagram, a hexagram, or a lollipop (or qoppa). We also consider "constrained" versions of the long-legged letters A, H, L, T, and X. In most cases we are able to determine the maximum number of pieces, although for the constrained A and the lollipop we can only give bounds.

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David O. H. Cutler, Jonas Karlsson, Neil J. A. Sloane. 2025-11-19. Cutting a Pancake with an Exotic Knife. https://arxiv.org/abs/2511.15864

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