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Exercise 11

Avg difficulty 2.5

A restaurant chef has designed a new set of dishes for his menu. His set of dishes contains 1010 main courses, and he will select a subset of them to place on the menu each night. To ensure variety of main courses for his patrons, he wants to guarantee that a night's menu is neither completely contained in nor completely contains another night's menu. What is the largest number of menus he can plan using his 1010 main courses subject to this requirement?

Keller & Trotter, Applied Combinatorics, Partially Ordered Sets — Exercises, Exercise 11

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Adapted from Applied Combinatorics © 2006–2025 Mitchel T. Keller, William T. Trotter. Licensed under CC BY-SA 4.0. Source: Applied Combinatorics. Imported at revision 07286c4.