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As part of the QED-it team - I hope you enjoy and we'd love any feedback :)
The solution to 1.1 is incomplete - Alice can set p=1 and q=n
Ah! It's one thing to be able to answer the question and another to show that the proposed solution is not good enough :-)

Thanks for the heads up - we should have specified this constraint about p and q.

I was confused how this related to graph theory until I realized "snark" is overloaded in mathematics,

1. Succinct Non-interactive ARgument of Knowledge https://en.wikipedia.org/wiki/Non-interactive_zero-knowledge...

2. Simple, connected, bridgeless cubic graph with chromatic index equal to 4 https://en.wikipedia.org/wiki/Snark_(graph_theory)

3. SRI's New Automated Reasoning Kit https://en.wikipedia.org/wiki/SNARK_(theorem_prover)

4. 90° stable glider reflector http://conwaylife.com/wiki/Snark