Just a thought: could we unleash a deep learning agent into an environment that codifies all the rules of a given law/policy system (e.g. tax), and with an appropriate reward system, expose possible loopholes in the system more quickly?

Just stumbled upon some ongoing drama around the of Leicester's purging of pure maths staff (along with several other departments), apparently for the sake of changing research direction towards areas like data science + AI + computation (perhaps for profitability?)

Seems the uni's getting backlash + boycott reactions as expected, but dunno if that's gonna make them reverse

Some extra context:

- Players are totally free to say anything to convince others to accept/reject their offer, including lying or double-bluffing; they cannot peek at each other's plant tally though
- The players had already accrued some points from previous tasks in the episode, so they're not on equal standing and hence may have different levels of risk aversion

Interesting game from an episode of Kongen Befaler (Taskmaster Norway):

- Each player starts with 3 roses (R) and 3 cacti (C)
- On a player's turn, they secretly choose how many of their R and C to give away, then declare their intended recipient
- If the recipient accepts, the offer proceeds; if rejected, the player instead gets to double the plants they offered up
- After all players' turns, they're scored based on R - C possessed at the end

frontiersin.org/articles/10.33

An article looking into the pedagogical practices in online courses @ USP suggests a dominance of conventional methods less interactive & engaging compared to other disciplines. Also seems to recommend more interactivity like frequent online assessments + collaborative activities, especially helpful for a dispersed group of learners.

You people celebrating Pi Day on 14 Mar or Tau Day on 28 Jun, are pushing MM-DD dates in a world generally more agreed on DD-MM(M)

We should have more representation for mathsy dates in DD-MM (only one that comes to mind so far is 22/7 for pi approx)

Random idea: if we scrape the abstracts of maths pre-prints and use them to train a Markov chain generator, we might be able to generate funny hypothetical pre-print ideas

Problem is being able to ensure that whatever $$\LaTeX$$ syntax is in the output isn't broken

So I've been mildly aware of the scandal surrounding the based on extremely slim odds, but it's also nice seeing Matt Parker's explanation as a non-playing mathematician who knows his way around enough

Each round, 5 players each secretly decide on a number from 1-99. Then revealing their numbers sequentially from player #1 to #5,

- if a player is higher than the one before them, both score +1
- if instead there is an exact match, both lose ALL current points

(Wrapping around means that #5 is before #1)

Is there any viable strategy for getting the most points depending on position? Especially since players #1 & #5 have a lower max win per round...

I am sure someone has posted this already but in my true mathematical geeky side....

2021 is not prime :(
It is the product of two consecutive primes :)
(43 and 47)
It only has 4 divisors. For some reason that makes me happy, well in a mathematical sense.

Yes, New Years Eve suddenly made me work this out...

Been watching some episodes of Taskmaster, and there's an interesting game involved in one episode:

5 players have 100 seconds to each secretly decide on a number from 1 to 5. After 100 seconds, the person with the lowest *unique* number in the round wins. If no such winner exists, new rounds are played until a win.

(The show let players indicate their numbers using donuts on their sticks)

Wonder what kind of viable strategies arise from this?

I think it's not too hard to come up with a arrangement for a given group such that everyone is connected by just one cycle... but I've been wondering about a "Double Secret Santa":

How do you asssign each person in a group to two separate recipients and two other anonymous gifters (that aren't also the aforementioned recipients), and ensure the least number of cycles formed by this assignment?

(Or course this group needs to have at least 5 people for this to work)

I think quite a number of us here are familiar with the song "12 Days of " and its relation with triangular numbers, so I've been wondering whether any other Xmas tunes have mathematical concepts tucked away in their lyrics

A little messing around with a tree sequence: starting with the first three leaf layers (*) in the 1st tree (n=1), add the next three layers by repeating that stack but 1 wider:

$\begin{matrix}\star\\*\\**\\***\\|\end{matrix}\quad \begin{matrix}\star\\*\\**\\***\\**\\***\\****\\|\end{matrix}\quad \begin{matrix}\star\\*\\**\\***\\**\\***\\****\\***\\****\\*****\\|\end{matrix}$

How many characters ($$\star,*,|$$) are needed to make the nth Xmas tree?

A problem from a drills book for Primary 1 (i.e. 7-year-old) students in has drummed up a bit of discussion among parents online:

$\begin{bmatrix}4 & 5 \\ 7 & 6\end{bmatrix} \ \begin{bmatrix}7 & 8 \\ 10 & 9\end{bmatrix} \ \begin{bmatrix}? & 11 \\ 8 & 12\end{bmatrix}$

Even though there's only supposed to be one answer, people have managed to come up with different plausible solutions, bringing into question the point of testing kids on "read the setter's mind" problems

The problem: imagine a circular fence that encloses one acre of grass. If you tie a goat to the inside of the fence, how long a rope do you need to allow the animal access to exactly half an acre?

Ingo Ullisch seems to have come up with the first exact solution to this puzzle, but it involves contour integrals and several trig terms, so we can only still compute a nunmerical approximation:

quantamagazine.org/mathematici

"Linking with Knowledge Graphs - Link Discovery for Schema-Agnostic Volunteered Geographic Information"

arxiv.org/pdf/2011.05841.pdf

(Here they test linking with and )

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