Deceptive Dice

Here an interesting riddle:

The Terrible Twins, Innumeratus and Mathophila, were bored. “I know”, said Mathophila brightly. “Let’s play dice!”
“Don’t like dice.”
“Ah, but these are special dice”, said Mathophila, digging them out of an old chocolate box. One was red, one yellow and one blue.

Innumeratus picked up the red dice. “There’s something funny about this one”, he said. “It’s got two 3’s, two 4’s and two 8’s.” “They’re all like that”, said Mathophila carelessly. “The yellow One has two 1’s, two 5’s and two 9’s – and the blue one has two 2’s, two 6’s and two 7’s.”

“They look rigged to me”, said Innumeratus, deeply suspicious. “No, they’re perfectly fair. Each face has an equal chance of turning up.”

“How do we play, anyway?”

“We each choose a different one. We roll them simultaneously, and the highest number wins. We can play for pocket money.” Innumeratus looked sceptical, so his sister quickly added: “Just to be fair, I’ll let you choose first! Then you can choose the best dice!”

“Weeelll … ” said Innumeratus, hesitating.

Should he play? What is so special about the dice?

Ian Stewart: “Professor Stewarts mathematisches Sammelsurium”, Rowohlt Taschenbuch Verlag, 2011.

Source featured image: gartentraum.de.

Hint: Click here to get a hint.

In a Nutshell

To prepare for exams, I usually create summaries that cover the entire content of the lecture. I put a lot of thoughts into what to include and what to omit, so that the summaries are reasonably complete but still clearly laid out. That’s why I’ve decided to share them. If you’re interested in what is covered in particle physics lectures at ETH Zürich, if you fancy hand-written QFT or particle physics summaries or if you just want to get an impression of physics lectures in general, take a look!

(These lectures are part of the MSc Physics and MSc High Energy Physics at ETH Zurich.)

Happy 2020!

I wish you all a Happy New Year! To start the year with a bang, check out my digital New Year’s card featuring a scientifically accurate electron explosion!


The simulation (implemented in COMSOL Multiphysics 5.4) involves 2020 electrons that are placed randomly in a “2020”-shaped geometry. Since the electrons repel each other via the electromagnetic force, they fly apart. Their speeds are indicated by the colors (in km/s). The simulation running backwards on the New Year’s card can be seen as (i) a metaphor for 2020 taking shape, (ii) a neat demonstration of T-symmetry of electromagnetism or (iii) a heresy to the Second Law of Thermodynamics.

It’s an ambush, Mr. Holmes

I am a huge fan of the Sherlock Holmes stories by Sir Arthur Conan Doyle, particularly in the form of audiobooks. A special hobby of mine is to listen to the first half of an audiobook, then to pause it and to draw my own conclusions before listening to the rest. Following this habit, I discovered a very interesting peculiarity in The Valley of Fear today.

Continue reading “It’s an ambush, Mr. Holmes”