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How-many-planes-can-pass-through-vertices-of-a-cube-a-when-each-plane-contains-at-least-three-vertices-b-when-each-plane-contains-exactly-four-vertices-c-Could-we-say-that-a-plane-can-pass-at-mo




Question Number 5539 by Rasheed Soomro last updated on 19/May/16
How many planes can pass through  vertices of a cube,  a) when each plane contains at least  three vertices.  b) when each plane contains exactly  four vertices.  c) Could we say that a plane can pass  at most four vertices?
$$\mathrm{How}\:\mathrm{many}\:\boldsymbol{\mathrm{planes}}\:\mathrm{can}\:\mathrm{pass}\:\mathrm{through} \\ $$$$\boldsymbol{\mathrm{vertices}}\:\mathrm{of}\:\mathrm{a}\:\boldsymbol{\mathrm{cube}}, \\ $$$$\left.{a}\right)\:\mathrm{when}\:\mathrm{each}\:\mathrm{plane}\:\mathrm{contains}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{least}} \\ $$$$\boldsymbol{\mathrm{three}}\:\boldsymbol{\mathrm{vertices}}. \\ $$$$\left.{b}\right)\:\mathrm{when}\:\mathrm{each}\:\mathrm{plane}\:\mathrm{contains}\:\boldsymbol{\mathrm{exactly}} \\ $$$$\boldsymbol{\mathrm{four}}\:\boldsymbol{\mathrm{vertices}}. \\ $$$$\left.{c}\right)\:\mathrm{Could}\:\mathrm{we}\:\mathrm{say}\:\mathrm{that}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{can}\:\mathrm{pass} \\ $$$$\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{most}}\:\boldsymbol{\mathrm{four}}\:\boldsymbol{\mathrm{vertices}}? \\ $$

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