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Using a zero-knowledge protocol to prove you can solve a sudoku

I’ve just uploaded to youtube a video I made with Katie Steckles to demonstrate why zero-knowledge protocols exist and how one works.

Katie is a habitual liar, so we followed the zero-knowledge protocol described in the paper, “Cryptographic and Physical Zero-Knowledge Proof Systems for Solutions of Sudoku Puzzles” which you can download from http://www.mit.edu/~rothblum/papers/sudoku.pdf

By following this protocol, Katie can prove that she isn’t lying to me about being able to solve the puzzle, without revealing anything about how she solved it.

The paper I mentioned, “How to explain zero-knowledge protocols to your children” is an excellent explanation of the ideas behind zero-knowledge proof.

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Fractal dimension in IKEA

A long time ago, I realised that IKEA’s shopfitters must be experts in fractal dimension – they manage to lay out their shop so that you have to walk past every single thing they’re selling. You can’t just nip into IKEA – you have to go through the whole hour-long “It’s A Small World” of affordably wobbly furniture even if all you want is some kitchen utensils from the bit at the end.

I’d been meaning to add something about this to the Maths in the City site but it required going in to IKEA and taking a picture of their floor plan for illustration.

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Interesting Esoterica Summation

I feel like it’s time to do another summary of my recent additions to the Interesting Esoterica collection.

A reminder of what it’s all about: every now and then I encounter a paper or a book or an article that grabs my interest but isn’t directly useful for anything. It might be about some niche sub-sub-subtopic I’ve never heard of, or it might talk about something old from a new angle, or it might just have a funny title. I put these things in my Interesting Esoterica collection on Mendeley.

In this post the titles are links to the original sources, and I try to add some interpretation or explanation of why I think each thing is interesting below the abstract.

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Putting all the world’s water in buckets

Following this pair of tweets about water:

A bucket full of water contains more atoms than there are bucketfuls of water in the Atlantic Ocean

— The QI Elves (@qikipedia) February 5, 2012

.@qikipedia There are 10,000× more molecules per pint of water than pints of water on earth. (3×10^21 pints/earth vs 2×10^25 molecules/pint)

— Matt Parker (@standupmaths) February 5, 2012

The obvious question is, at what point are the two numbers the same? Or,

If you put all the Earth’s water into containers of the same size so that each container carries as many atoms of water as there are containers, how big is each container?

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Newcastle MathsJam January 2012 Recap

January’s MathsJam was a bit massive. It’s now a week later and I’ve only just gathered enough thoughts together to do this writeup.

There were nine of us this month, all but one of whom either maths students or lecturers. A major theme of the night was of professional mathematicians or nearly-professional mathematicians forgetting basic high-school methods. This led to quite an intense session of puzzling and proving.

Things didn’t start out that way, though. A few weeks ago I found the website of a mathematician in Illinois called Alan Schoen, and his page about Lominoes. They’re a pretty interesting set of shapes!

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