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.
From: N. J. A. Sloane [view email]
[v1]
Wed, 19 Nov 2025 20:41:39 UTC (321 KB)
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Sat, 20 Dec 2025 18:24:38 UTC (323 KB)
[v3]
Sun, 19 Apr 2026 20:44:01 UTC (320 KB)
[v4]
Sat, 18 Jul 2026 02:11:03 UTC (325 KB)
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