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Is it possible to arrange seven points in a plane so that any subset of three points will contain at least one pair that is exactly 1cm apart?[/vc_column_text][/vc_column][/vc_row][vc_row][vc_column][lvca_accordion][lvca_panel panel_title="Reveal Solution"]Yes – the diagram below shows a possible arrangement.
{B, C, D, E, F, G} has a pair from either {B, C, D} or {E, F, G} which will be 1cm apart. If A is included then either B, C, E or F is there (which are all 1cm from A) or both D and G are there which are 1cm from each other.
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Problem Page Coordinator: Stephen Lee CMath MIMA – Mathematics in Education and Industry
Acknowledgement: The IMA are indebted to MEI for sourcing and supplying Mathematics Today with these well-known puzzles.
First published in Mathematics Today (December 2015)
Is it possible to arrange seven points in a plane so that any subset of three points will contain at least one pair that is exactly 1cm apart?[/vc_column_text][/vc_column][/vc_row][vc_row][vc_column][lvca_accordion][lvca_panel panel_title="Reveal Solution"]Yes – the diagram below shows a possible arrangement.
{B, C, D, E, F, G} has a pair from either {B, C, D} or {E, F, G} which will be 1cm apart. If A is included then either B, C, E or F is there (which are all 1cm from A) or both D and G are there which are 1cm from each other.
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