1) Show that in any positioning of 17 rooks on an 8-by-8 chessboard, there must be at least three rooks none of which threaten each other (i.e. no two of which lie in the same row or column). 2) Sixteen people must sit in a row of eighteen chairs. Prove that somewhere in the row there must be six adjacent chairs all occupied.
1) Show that in any positioning of 17 rooks on an 8-by-8 chessboard, there must be at least three rooks none of which threaten each other (i.e. no two of which lie in the same row or column). 2) Sixteen people must sit in a row of eighteen chairs. Prove that somewhere in the row there must be six adjacent chairs all occupied.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.3: Informal Geometry And Measurement
Problem 9E: Must two different points be collinear? Must three or more points be collinear? Can three or more...
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