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Show that for all integers \(n>0\) it is possible to paint all the sides of all the small triangles red. - MathsGee Science Technology & Innovation Forum
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Three coins, \(A, B, C\) are situated one at each vertex of an equilateral triangle of side \(n\). The triangle is divided into small equilateral triangles of side 1 by lines parallel to the sides. Initially, all the lines of the figure are blue. The coins move along the lines, painting in red their trajectory, following the two rules:
(i) First coin to move is \(A\), then \(B\), then \(C\), then again \(A\), and so on. At each turn, a coin paints exactly one side of one of the small triangles.
(ii) A coin can not move along a segment that is already painted red, but it can stay at an endpoint of a red segment, not necessarily alone.

Show that for all integers \(n>0\) it is possible to paint all the sides of all the small triangles red.

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /home/customer/www/mathsgee.com/public_html/qa-include/qa-theme-base.php on line 160

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /home/customer/www/mathsgee.com/public_html/qa-include/qa-theme-base.php on line 162
in Mathematics by Platinum (138,598 points) | 25 views

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /home/customer/www/mathsgee.com/public_html/qa-include/qa-theme-base.php on line 935

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /home/customer/www/mathsgee.com/public_html/qa-include/qa-theme-base.php on line 935

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