Joining numbers using edges

Geometry Level pending

Is it possible to join each pair of the same numbers (example 0 and 0) by an edge if the following conditions observed? (i) There is no crossing between the edge; (ii) the edges must within the blue circle; (iii) the numbers (0, 1, 2, .., 6) are joined at the end of the edge, not any other part of it.

Remark: different drawing of an edge will produce different way (if it is possible)

No, it is not possible. Yes, there are finitely many and more one way to do it. Yes, there are infinitely many ways to do it. Yes, there is a unique way to do it.

Chan Lye Lee by Chan Lye Lee , 44, Singapore

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1 solution

Chan Lye Lee
Jun 21, 2020

Two different possible ways are as shown. (Spot the difference: edges joining 6 and 6, 5 and 5, are different)

There are infinitely many ways by just changing this small path here, hence there are infinitely many ways to do it.

Discussion can be found in this video .

0 Helpful 1 Interesting 0 Brilliant 0 Confused

Nice problem! I realise there are infinitely many paths because of the embedding in R 2 \mathbb{R}^2 , but is there a way to count the essentially topologically distinct paths? I'm not quite sure how to define the question rigorously - perhaps in terms of which pairs of numbered dots each path passes between. You've given two distinct solutions above; are there others?

Chris Lewis - 11 months, 3 weeks ago

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