Odds and Evenings

The boys return to think about the structure of a quiz show round, they learn how to queue effectively and they investigate the best tunings for guitars. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Only Connect Loops Adding a Teller Alternative Tunings Show Notes Queuing Blog (https://www.johndcook.com/blog/2008/10/21/what-happens-when-you-add-a-new-teller/) Cabbage Tuning (https://www.youtube.com/watch?v=cB54IWMWVrc) Under the Bridge Tuning (https://www.youtube.com/watch?v=Daw93bRHe4Y) David's Kingdom Heart Video Series (https://www.youtube.com/watch?v=f11crL1IxSA) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Infeasible App Ideas by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys are in the same room, and they have a guest! They talk about an awful tennis tournament mixup, a teeny tiny card game and the primest day of the year. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Quantum Go Fish Amateur-Professional Tennis Tournament Problem Prime Day Show Notes Some divisbility criteria (https://brilliant.org/wiki/divisibility-rules/) The Trachtenburg System (https://en.wikipedia.org/wiki/Trachtenberg_system) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Guest Matthew - http://mscroggs.co.uk/ Editing by Alex Invisible playing cards supplied by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323 Special Guest: Matthew Scroggs.

The boys sit down with an infinite box of resistors, worry just how diverse their business is and think through the peculiar physics of balloons. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Resistor Mathematics How to Measure Diversity Balloon in a Car Show Notes The XKCD Resistor Problem we Mention (https://xkcd.com/356/) An article I wrote which uses Δ-Y transformations for calculating resistance (http://www.alaricstephen.com/main-featured/2017/10/15/gchq-resistor-puzzle-solution) The Diversity Formula (http://www.countrysideinfo.co.uk/simpsons.htm) An article I wrote about Simpson's Paradox (http://www.alaricstephen.com/main-featured/2016/12/11/simpsons-paradox) The Sprinkler Problem (https://en.wikipedia.org/wiki/Feynman_sprinkler) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Fish schematics by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

Here's something a little different. Over at Aperiodical they are running the Big Internet Math Off 2019 (https://aperiodical.com/2019/06/announcing-the-big-internet-math-off-2019/), where 16 mathematicians present pitches to compete in a tournament. We were very pleased to be nominated to take part. For this round we thought we'd do what we do best, albeit in smaller, snack sized portion. We are up against Grant Sanderson of 3Blue1Brown (https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw?&ab_channel=3Blue1Brown) which is a channel that we both love. You can find both of our pitches here (https://aperiodical.com/2019/07/the-big-internet-math-off-2019-group-1-grant-sanderson-vs-alaric-stephen/), where if you like what you hear we would very much appreciate your support by voting for Alaric. Most importantly, here is the file (https://drive.google.com/open?id=1SKMl1Fh6CtW2nFcSBPxSZuiuLLrMelWn) that my student Ed Ceney created so you can try to come up with the best strategy yourself. The paper outlining the original experiment can be found here (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2856963). Normal episodes will resume shortly.

The boys are back for season two! They try ramping Pascal's Triangle up a couple of dimensions, consider the physics of how we control volume and attempt to help out someone with a fishy problem. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Pascal's Pyramid Sound Quality Fish Tank Siphoning Show Notes Cuboctohedron Stacking (https://robertlovespi.net/2014/03/25/a-space-filling-pair-of-polyhedra-the-cuboctahedron-and-the-octahedron/) Sphere Packing Systems (https://en.wikipedia.org/wiki/Close-packing_of_equal_spheres?fbclid=IwAR3pUsuDc8I0u-EK8WOeh0C5KgRdgH7XWd1_QoDRx3qTssLVqd9AQI7UPDA) Colouring in Pascal's Triangle in mod 3, 4 and 5 (https://www.maa.org/press/periodicals/loci/joma/patterns-in-pascals-triangle-with-a-twist-first-twist-what-is-it) Sierpinski's Pyramid (https://www.researchgate.net/figure/Ray-tracing-Figure-13-The-Sierpinski-Pyramid_fig2_260126327) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Quasi-analytic classes with respect to logarithmically convex sequences by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys help organise a rugby training scheme, set robots upon an infinite hotel and discover some lovely patterns in the probability of Snakes and Ladders. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Rugby Training Problem Busy Beavers Gamble Shambles Show Notes Articles written by Alaric on Langton's: * Loops (Introduction) (http://www.alaricstephen.com/main-featured/2017/6/27/langtons-loops) * Loops (Evolving) (http://www.alaricstephen.com/main-featured/2017/6/27/improvements-to-langtons-loops) * Ant (http://www.alaricstephen.com/main-featured/2016/12/13/langtons-ant) Busy Beaver on Wikipedia (https://en.wikipedia.org/wiki/Busy_beaver) Noether's Theorem (https://en.wikipedia.org/wiki/Noether%27s_theorem) The Music Episode (http://www.oddsandevenings.com/21) Maths Jam (that you should totally be attending) (https://mathsjam.com/find-a-jam/) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Appreciation of the phrase Busy Beavers by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys partake unto an unwavering curiousity as to who is friends with whom. Infinite-dimensional animals are discussed, and they ponder the potentially undue rewards of chess pros. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Ramsey's Theorem Scaling Sports and Games Rating Show Notes Scale by Geoffrey West (https://www.penguinrandomhouse.com/books/314049/scale-by-geoffrey-west/9780143110903/) Goblin Game Spreadsheet (https://drive.google.com/file/d/19K-4NPK5wK-sRx6NC16LNfaq4rgXMZaG/view?usp=sharing) Quantum Computing Video (https://youtu.be/F_Riqjdh2oM) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex The actual good questions by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys find themselves on the wrong side of the mathematical orthodoxy, rejecting the concepts of distance and angles, before immediately forgetting about that and using distances and angles to solve a problem. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Rational Geometry Goblin Game Car Pool Problem Show Notes Introduction to Rational Geometry Overview by Norman Wildberger (https://youtu.be/dVk3CpjHR4Y?t=3m19s) The Video in his Lecture Sequence which covers some of the topics we discussed on our show (https://www.youtube.com/watch?v=ZYWHfvij94U&list=PL3C58498718451C47&index=2&ab_channel=njwildberger) The 5 Laws of Rational Geometry (https://en.wikipedia.org/wiki/Rational_trigonometry#Laws_of_rational_trigonometry) Goblin Game (http://gatherer.wizards.com/Pages/Card/Details.aspx?multiverseid=8902) New Prime Discovered (https://www.mersenne.org/) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Calls for radical overthrowing of the establishment by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

Here's a copy of the puzzle that Alaric wrote for the conference: Chyptic Chossword (https://uploads.fireside.fm/images/b/b3fcc274-493e-4d2e-87a4-3d1ae3127c05/t4Kb6p0j.png) The boys play games, join a secret circle and put up the Christmas lights :) Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Wythoff's Game A Christmas Cipher Zig Zag Lights Show Notes Wythoff's Game on Wikipedia (https://en.wikipedia.org/wiki/Wythoff%27s_game) A good blog article about Wythoff's Game and the Golden Ratio (http://math450games.blogspot.com/2017/02/wythoffs-queens-and-wythoffs-nim.htm) Little Orphan Annie Scene (https://www.youtube.com/watch?v=zdA__2tKoIU) Little Orphan Annie image album (https://imgur.com/a/B9R79kn) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Invention of Christmas (the concept thereof) by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys celebrate a year of the podcast, try to get a hold on some of the weirder polygonal numbers and debrief after big maths jam. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Trapezium Numbers Shamir's Shared Secrets Vampire and Werewolf Lies Show Notes Catriona Shearer's Geometry Puzzles on Twitter (https://twitter.com/Cshearer41) Mathigon's Tweet about Trapezium Numbers (https://twitter.com/MathigonOrg/status/1070302146632081409?s=09) An Article on Properties of Trapezium Numbers (https://www.hindawi.com/journals/ijmms/2017/4515249/#B4) Alaric's Lock Gates Article (http://www.alaricstephen.com/main-featured/2017/5/1/lock-gates?rq=key) A Good Quality Shamir's Shared Secrets Article (https://ericrafaloff.com/shamirs-secret-sharing-scheme/) The Vampire and Werewolf MAT Question (https://www.cs.ox.ac.uk/admissions/undergraduate/how_to_apply/MAT2015.pdf) The Answers to the MAT Question (https://www.maths.ox.ac.uk/system/files/attachments/websolutions15_1.pdf) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Silver Service at the Vampire-Werewolf Symposium by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys get to the bottom of a neat pattern that suddenly breaks, contort their limbs into strange shapes in the name of Plato and attempt a very satisfying problem involving some spiders and an ant. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Factorial Terminating Digits Making Polyhedra with your Limbs Spiders and an Ant Pursuit Puzzle Show Notes Nice PDF of the Solution to the Partitions Problem by André Malraux (https://ufile.io/twukd) Alaric's Puzzle from the Conference (https://twitter.com/OddsAndEvenings/status/1064153315280330752) Platonic Solids to Stare at during Sections 2 and 3 of the Show (https://upload.wikimedia.org/wikipedia/commons/d/d3/Platonic_solids.jpg) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Fervent attempts to keep on top of responding to emails for the show by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys get as spooky as they can with cellular automata, have a maths conversation about maths conversations and can't get past the fact that Brunnian and Borromean sound too similar. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Zombies and Vampires The Maths of Conversations Brunnian Pumpkin Carving Show Notes Follow Up Maths Jam Annual Gathering Page (https://www.solipsys.co.uk/cgi-bin/MJ_Wiki.py?FrontPage) The Shade (Alex's New Podcast) (https://hacking.finance/read/?c=the-shade) Maths From the Show SIR Model Introduction by Alaric (http://www.alaricstephen.com/main-featured/2016/9/24/modelling-a-pandemic) SIR Model You Can Play With (https://docs.google.com/spreadsheets/d/1HxS1GttDPT8eDOhTIfOYckueArSJjGb5VfOr1hgqLno/edit?usp=sharing) Borromean Rings (https://en.wikipedia.org/wiki/Borromean_rings) Brunnian Links (https://en.wikipedia.org/wiki/Brunnian_link)(more generalised) Pochhammer's Countour (https://en.wikipedia.org/wiki/Pochhammer_contour) A Classic Video on Brunnian Links (https://www.youtube.com/watch?v=heKK95DAKms&ab_channel=Vihart) (in the form of snakes), by Vi Hart Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Following of the brief: bring halloween problems by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys settle a dicussion about a bike that Alaric has been aching to talk about for a fortnight, Alex finally brings up music and then they both dive down the Gödel rabbit hole with some puzzles. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Bike Pedals Time Signatures Taking an Offer Puzzles Show Notes Follow Up Visualisation of the Codepad Solution from Tom Verduyn (https://bl.ocks.org/TVerduyn/raw/4935615ba55a2c0b73b2550e0eb8764d/) Maths Jam Annual Gathering Page (https://www.solipsys.co.uk/cgi-bin/MJ_Wiki.py?FrontPage) The Shade (Alex's New Podcast) (https://hacking.finance/read/?c=the-shade) Maths From the Show Visuals of the Two Cycloids Mentioned: Prolate (http://mathworld.wolfram.com/ProlateCycloid.html) and Curtate (http://mathworld.wolfram.com/CurtateCycloid.html) Video of the Bike Moving (https://twitter.com/SingMathsJam/status/1042057017148334080) Unusual Time Signatures (https://en.wikipedia.org/wiki/List_of_musical_works_in_unusual_time_signatures) Forever Undecided: A Puzzle Guide to Gödel (https://www.amazon.co.uk/Forever-Undecided-Puzzle-Guide-Godel/dp/0192801414) The book I talk about in the third part of the show. It's great. The Gödel Sentence on Wikipedia (https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Truth_of_the_Gödel_sentence) (Related to the puzzle) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Incomplete knowledge of incompleteness theorems by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys design algorithms to generate puzzles on graphs, spiral out into some polar coordinate calculus and gallop their way through some juggling notation. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Untangling Planar Graphs The Length of Spirals Juggling and Horse Gaits Show Notes A Picture of Untangle (http://www.gameclassification.com/files/games/Untangle.png) The Criteria for Planarity (https://en.wikipedia.org/wiki/Kuratowski%27s_theorem) The Two Spirals in Desmos (a graphing calculator) (https://www.desmos.com/calculator/xqqafvcbf9) Arc Length in Polar Form Derivation (http://sites.millersville.edu/bikenaga/calculus/arc-length-in-polar/arc-length-in-polar.html) Jakob Bernoulli's Gravestone (https://www.flickr.com/photos/deaddogbarking/4545328000) Horse Gaits on Wikipedia (https://en.wikipedia.org/wiki/Horse_gait) Negative Juggling Simulator (http://juggle.wikia.com/wiki/Impossible_Siteswap_Animator) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Rather fitting spiral anecdote by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys delve into some stats and game theory problems, ending with a classic from Conway. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Dominion Probabilities The Cheapest Beer in Prague The Angel Problem Show Notes Dominion Probabilities Article (http://www.alaricstephen.com/main-featured/2016/11/28/dominion-probabilities) The Generalised Coupon Collecting Formula in Wolfram Alpha (www.wolframalpha.com) Type this into input: sum from j=0 to 25 of ((-1)^(j)(25 choose j)(((25-j) choose 10)/(25 choose 10))^8) (I couldn't directly link because the % signs in the URL were messing up our site linking. Apologies for the mess. The Secretary Problem (https://en.wikipedia.org/wiki/Secretary_problem) The Angel Problem (by Alaric) (http://www.alaricstephen.com/main-featured/2017/7/12/the-angel-problem) James Grime's Video on the Codepad Problem (https://www.youtube.com/watch?v=iPLQgXUiU14&ab_channel=singingbanana) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Back to school vocals by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys move seemlessly between high philosophy and pirate jokes in this eclectic episode. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Keypad Code Guessing Platonism vs Formalism Pirate Plunder Puzzle Show Notes Pirate Plunder Puzzle (http://www.alaricstephen.com/main-featured/2017/4/10/the-pirate-puzzle) Prisoners in Rainbow Hats (http://www.alaricstephen.com/main-featured/2017/6/13/prisoners-in-rainbow-hats) Z-Order Curves (https://en.wikipedia.org/wiki/Z-order_curve) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Dreams of being a philosopher pirate by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys try their hands at problems provided by the listeners in today's special episode. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Prisoners in Hats Kaprekar's Constant Generalised Egg Dropping Show Notes Prisoners in Rainbow Hats (http://www.alaricstephen.com/main-featured/2017/6/13/prisoners-in-rainbow-hats) Islander Paradox (http://www.alaricstephen.com/main-featured/2017/4/10/the-islander-paradox) Kaprekar's Constant (https://en.wikipedia.org/wiki/6174_(number)) General Egg Problem Solution (https://stackoverflow.com/questions/11603218/three-egg-problem#) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Too many Hat Problem anecdotes by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys both have problems which involve complicating the process of adding. Also snakes. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed FRACTRAN Negative Bases Polycube Snakes Show Notes FRACTRAN (https://en.wikipedia.org/wiki/FRACTRAN) Adding in Negative Bases (https://en.wikipedia.org/wiki/Negative_base#Addition) Quarter-Imaginary Base (https://en.wikipedia.org/wiki/Quater-imaginary_base) Fascinating Turing Complete Magic the Gathering (https://www.toothycat.net/~hologram/Turing/HowItWorks.html) Article on Polycube Snakes (http://www.alaricstephen.com/main-featured/2017/5/20/polycube-snakes) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Knuth Pronunciation by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys both choose to take a medley of problems on the same theme, then solve a puzzle ridiculously quickly. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Moving Sofa Problem Zero Knowledge Grab Bag The Fuse Problem Show Notes Moving Sofa Problem (https://en.wikipedia.org/wiki/Moving_sofa_problem) Kakeya's Needle (http://www.alaricstephen.com/main-featured/2016/10/13/kakeya-needle) Moser's Worm (http://www.alaricstephen.com/main-featured/2016/12/5/mosers-worm) Two Fuses Problem (http://www.alaricstephen.com/main-featured/2016/12/5/the-two-fuses-problem) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex All the right answers, but not the right right answers by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys go on serious diversions. Alex fails to use a computer properly. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Digital Mastermind Cheers p^2 - 1 mod 24 Show Notes Grover's Algorithm (https://en.wikipedia.org/wiki/Grover%27s_algorithm) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Puzzlemancy by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323