A conversation about mathematics inspired by a guitar. Presented by Katie Steckles and Peter Rowlett, with special guest Sam Hartburn.
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A conversation about mathematics inspired by a guitar. Presented by Katie Steckles and Peter Rowlett, with special guest Sam Hartburn.
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The recent preprint ‘You need 27 tickets to guarantee a win on the UK National Lottery‘ by David Cushing and David I. Stewart presents a list of 27 lottery tickets which will guarantee to match at least two numbers on the UK National Lottery, along with a proof that this is the minimum number you need to buy. The argument is clever and makes delightful use of the Fano plane.
I wrote some Python code that runs all 45,057,474 possible draws against these 27 tickets.
All draws had between 1 and 9 winning tickets from the set (crucially, none had zero!). Obviously for 27 of the draws one of the winning tickets matched all six numbers, but about 75% of the draws saw a maximum of 2 balls matched by the winning tickets, and a further 23.5% had at most 3 balls matched. This means almost 99% of the time the 27 tickets match just two or three balls, earning prizes which may not exceed the cost of the 27 tickets! (I recommend reading Remark 1.2 in the paper.)
More findings and my code on GitHub.
Update 1: Tom Briggs asked what’s the expected return for buying these 27 tickets. I think the average return is about £20, which is a £34 loss (and of course this is an average from a set of numbers that includes some big wins). Assumptions and details in the GitHub.
Update 2: Matt Parker prompted me to investigate what percentage of draws end in profit. Even though 99% of the time the tickets match just two or three balls, if more than one ticket matches three balls that would still be a small profit. In fact, a profit is returned in 5% of draws, though as noted above the expected return is a loss. Matt included this result in a fun video about the 27 tickets. Again, assumptions and details in the GitHub.
A conversation about mathematics inspired by a 1960s game designed to teach set theory. Presented by Katie Steckles and Peter Rowlett.
On-Sets: A Vintage Set Theory Game by Peter Rowlett is free to read in Math Horizons.
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Maths news didn’t stop coming this month, and if you missed it, here was our coverage of the new Spectre aperiodic monotile, an improvement on the previous monotile discovery. Here’s some other news that happened in May and June which we didn’t otherwise cover here.
Vladimir Drinfeld and Shing-Tung Yau have been awarded the 2023 Shaw Prize for their contributions related to mathematical physics, to arithmetic geometry, differential geometry and Kähler geometry. (via the European Mathematical Society)
According to provisional 2023 entry data, mathematics remains the most popular choice at A level in England and Wales this year.
Ticket sales continue apace for this year’s TMiP maths communication conference, and in the meantime it’s inspired a nascent equivalent network for math communicators in the US – sign up if you’re an American math communicator who WLTM others.
There’s been a moderation strike at Stack Overflow, which includes Math Overflow, in response to AI-generated content policy changes. “Striking community members will refrain from moderating and curating content, including casting flags, and critical community-driven anti-spam and quality control infrastructure will be shut down.” (via theHigherGeometer)
There’s a free online IMA event, including a talk called ‘How Maths Helped Me to Annoy My Insurance Company’ by Victoria Sánchez Muñoz taking place at 5pm on Thursday 13 July.
Obviously the most important news this month is the new Rubik’s cube world record – it’s now possible for a human to solve the cube in as little as 3.13 seconds (furious they’ve skipped π seconds) and the GIF included in the article shows just how impressive the feat was.
And finally, this Nature article outlines how deep reinforcement learning has discovered faster sorting algorithms. Algorithms such as sorting or hashing are everywhere – used trillions of times a day, according to the article. This means even small efficiency improvements can be huge because of the scale, but these algorithms are so well-studied that further efficiency was difficult to imagine. DeepMind trained a deep reinforcement agent, AlphaDev, to work from scratch using assembly code to attempt to find a better sorting routine. The researchers reverse engineered the algorithms found by AlphaDev to C++ and found these led to performance improvements of “up to 70% for sequences of a length of five and roughly 1.7% for sequences exceeding 250,000 elements”. The Nature paper has details of the algorithmic improvements. The improved algorithms have already been implemented into the LLVM libc++ standard sorting library.
A conversation about mathematics and literature inspired by a book. Presented by Katie Steckles and Peter Rowlett with special guest Sarah Hart, author of Once Upon a Prime: The Wondrous Connections Between Mathematics and Literature.
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The UK Government have announced the first set of King’s Birthday Honours for King Charles III. Here’s our selection of particularly mathematical entries for this year. If you spot any more, let us know in the comments and we’ll add to the list.
Get the full list of honours on gov.uk.
A conversation about mathematics inspired by a Battenberg cake. Presented by Katie Steckles and Peter Rowlett.
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