You could probably go for the rest of the month without feeding the machine in the same way twice.
Can you feed the machine in a different way each day of the year?
You can find a longer version of this puzzle, including some follow-up questions to investigate, on the Wild Maths site. Wild Maths encourages students to explore maths beyond the classroom and is designed to nurture mathematical creativity. The site is aimed at 7 to 16 year-olds, but open to all. It provides games, investigations, stories and spaces to explore, where discoveries are to be made. Some have starting points, some a big question and others offer you a free space to investigate.
One interpretation of the strange theory of quantum mechanics is that
tiny particles can simultaneously exist in states that we would
usually deem mutually
exclusive. For example, an electron can be in two places at once, or a
radioactive atom can be both decayed an non-decayed at the same
time. It's only when we go to measure a system in
superposition, as this strange state is called, that reality
somehow "collapses" to one of the possibilities.
In 1935 the physicist Erwin Schrödinger, who made major
contributions to the theory of quantum mechanics, developed a thought experiment in order to demonstrate just how
counter-intuitive the idea of superposition is. We let him describe it
in his own words, taken from a translation of his 1935 paper:
One can even set up quite ridiculous cases. A cat is penned up
in a steel chamber, along with the following device (which must be
secured against direct interference by the cat): in a Geiger counter
there is a tiny bit of radioactive substance, so small, that perhaps
in the course of the hour one of the atoms decays, but also, with
equal probability, perhaps none; if it happens, the counter tube
discharges and through a relay releases a hammer which shatters a
small flask of hydrocyanic acid.
Thus, when an atom decays, poison will be released from the flask and the cat
killed. And here's the main point. If it is true that, as long as we
don't look, the system can evolve into a superposition state of atoms being simultaneously decayed and not decayed, then
it follows that, as long as we don't look, the cat will be simultaneously
dead and alive. Poor cat. Or should we say lucky cat?
Barrow has written a book about maths and the arts.
John D. Barrow, mathematician, cosmologist and boss of Plus, explores maths and the arts in a public talk in Cambridge on Monday, 02 November 2015.
Barrow will look at ways in which maths can shed light upon a range of questions in the arts and how problems of art and design inspire new mathematical questions. The canvas will be broadly drawn with examples from different areas of the arts, including painting, textual analysis, diamond cutting, Henry Moore's stringed figures, ballet, and even the best place to stand when viewing statues.
In this fascinating talk theoretical physicist Ben Allanach talks about the search for dark matter at the Large Hadron Collider, including a generous helping of information on the Higgs boson. Ben gave the talk on 19 June 2015 to an audience of school students aged 16-17 as part of a mathematics enrichment event at the University of Cambridge.
In this excellent talk the mathematician Vicky Neale gives a fascinating and easy-to-follow introduction to the prime numbers — from a thorough description of what they are, via the ancient proof that there are infinitely many, to the prime number theorem, the twin prime conjecture and more. By the end of this talk you hopefully agree with us, and Vicky, that the world would be a very boring place without primes.
Vicky gave this talk at the University of Cambridge on 19 June 2015 to an audience of Year 12 A-level Maths students (aged 16-17). It formed part of a mathematics enrichment day organised by the Millennium Mathematics Project with a special focus on encouraging creative mathematical thinking. For more on creative mathematics, visit Wild Maths.
Are you queueing in an airport, wondering if there is a better way to deal with the mass of humanity trying to board planes? Are you stuck at home wondering where the summer weather has gone? Would you like to see our information overloaded world in a more beautiful way? Do you think the world would be a better place if we made lovely maths, instead of war? Then you should book your place for the 2015 British Science Festival
This year the festival is in Bradford from 7-10 September. And, as well as delights in all areas of science, there is some fascinating maths to enjoy. In Advanced airports and on-time ambulances, Kevin Glazebrook and Vincent Knight will explain how number crunching improve holiday travel chaos in airports, and get you medical help in an emergency quicker. And on the subject of health, you can join in a mini-epidemic with Erin Lafferty as she reveals the medical secrets behind infection in Can maths decode infectious diseases?
Meanwhile scientist Martin Brinkworth, mathematician Simon Shepherd and artist Marcus Levine will show us the beautiful side of big data in Art and big data and explore what our innate appreciation of aesthetics in these representations can reveal. In Love and war: the mathematical way Hannah Fry will demonstrate the power of maths in understanding human behaviour in the rawest of human emotions. You can find out more about these and all the other fascinating events at the Festival website – booking is now open!