Eulero docet

Probability Level 1

Which of the following developements of the 5 platonic solids can be drawn without ever lifting the pencil from the sheet and without passing on the same edge twice?

A B C D E

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Matteo Benigni by Matteo Benigni , 21, Italy

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4 solutions

Oliver Papillo
Dec 23, 2016

For there to be an eulerian path , it must have a maximum of 2 nodes with odd degree. The only graph with this quality is C, therefore it is the answer.

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(The top of Figure E is missing an edge.)

Ben Reiniger - 4 years, 5 months ago
Green Lao
Sep 1, 2018

Please fix the Dodecahedron graph

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Cantdo Math
Apr 16, 2020

For C,it's vertices all have degree 4.Since 4 is even and number of vertices is 6,it satisfies both conditions.

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Davy Ker
Dec 27, 2017

Bit of a moot question given the previous one... The platonic solids have 3, 3, 4, 3, and 5-sided vertex figures respectively, so only the octahedron has and even number of edges at every vertex. So only the octahedron has an Euler circuit.

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